Calculus Examples

$lim_{t \to - \frac{3}{2}} (2 t^{5} - 3 t^{4} + 5 t^{3}) \cdot (t^{4} - t^{2})$

Step 1

Split the limit using the Product of Limits Rule on the limit as $t$ approaches $- \frac{3}{2}$ .

$lim_{t \to - \frac{3}{2}} 2 t^{5} - 3 t^{4} + 5 t^{3} \cdot lim_{t \to - \frac{3}{2}} t^{4} - t^{2}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $t$ approaches $- \frac{3}{2}$ .

$(lim_{t \to - \frac{3}{2}} 2 t^{5} - lim_{t \to - \frac{3}{2}} 3 t^{4} + lim_{t \to - \frac{3}{2}} 5 t^{3}) \cdot lim_{t \to - \frac{3}{2}} t^{4} - t^{2}$

Step 3

Move the term $2$ outside of the limit because it is constant with respect to $t$ .

$(2 lim_{t \to - \frac{3}{2}} t^{5} - lim_{t \to - \frac{3}{2}} 3 t^{4} + lim_{t \to - \frac{3}{2}} 5 t^{3}) \cdot lim_{t \to - \frac{3}{2}} t^{4} - t^{2}$

Step 4

Move the exponent $5$ from $t^{5}$ outside the limit using the Limits Power Rule.

$(2 {(lim_{t \to - \frac{3}{2}} t)}^{5} - lim_{t \to - \frac{3}{2}} 3 t^{4} + lim_{t \to - \frac{3}{2}} 5 t^{3}) \cdot lim_{t \to - \frac{3}{2}} t^{4} - t^{2}$

Step 5

Move the term $3$ outside of the limit because it is constant with respect to $t$ .

$(2 {(lim_{t \to - \frac{3}{2}} t)}^{5} - 3 lim_{t \to - \frac{3}{2}} t^{4} + lim_{t \to - \frac{3}{2}} 5 t^{3}) \cdot lim_{t \to - \frac{3}{2}} t^{4} - t^{2}$

Step 6

Move the exponent $4$ from $t^{4}$ outside the limit using the Limits Power Rule.

$(2 {(lim_{t \to - \frac{3}{2}} t)}^{5} - 3 {(lim_{t \to - \frac{3}{2}} t)}^{4} + lim_{t \to - \frac{3}{2}} 5 t^{3}) \cdot lim_{t \to - \frac{3}{2}} t^{4} - t^{2}$

Step 7

Move the term $5$ outside of the limit because it is constant with respect to $t$ .

$(2 {(lim_{t \to - \frac{3}{2}} t)}^{5} - 3 {(lim_{t \to - \frac{3}{2}} t)}^{4} + 5 lim_{t \to - \frac{3}{2}} t^{3}) \cdot lim_{t \to - \frac{3}{2}} t^{4} - t^{2}$

Step 8

Move the exponent $3$ from $t^{3}$ outside the limit using the Limits Power Rule.

$(2 {(lim_{t \to - \frac{3}{2}} t)}^{5} - 3 {(lim_{t \to - \frac{3}{2}} t)}^{4} + 5 {(lim_{t \to - \frac{3}{2}} t)}^{3}) \cdot lim_{t \to - \frac{3}{2}} t^{4} - t^{2}$

Step 9

Split the limit using the Sum of Limits Rule on the limit as $t$ approaches $- \frac{3}{2}$ .

$(2 {(lim_{t \to - \frac{3}{2}} t)}^{5} - 3 {(lim_{t \to - \frac{3}{2}} t)}^{4} + 5 {(lim_{t \to - \frac{3}{2}} t)}^{3}) \cdot (lim_{t \to - \frac{3}{2}} t^{4} - lim_{t \to - \frac{3}{2}} t^{2})$

Step 10

Move the exponent $4$ from $t^{4}$ outside the limit using the Limits Power Rule.

$(2 {(lim_{t \to - \frac{3}{2}} t)}^{5} - 3 {(lim_{t \to - \frac{3}{2}} t)}^{4} + 5 {(lim_{t \to - \frac{3}{2}} t)}^{3}) \cdot ({(lim_{t \to - \frac{3}{2}} t)}^{4} - lim_{t \to - \frac{3}{2}} t^{2})$

Step 11

Move the exponent $2$ from $t^{2}$ outside the limit using the Limits Power Rule.

$(2 {(lim_{t \to - \frac{3}{2}} t)}^{5} - 3 {(lim_{t \to - \frac{3}{2}} t)}^{4} + 5 {(lim_{t \to - \frac{3}{2}} t)}^{3}) \cdot ({(lim_{t \to - \frac{3}{2}} t)}^{4} - {(lim_{t \to - \frac{3}{2}} t)}^{2})$

Step 12

Evaluate the limits by plugging in $- \frac{3}{2}$ for all occurrences of $t$ .

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Step 12.1

Evaluate the limit of $t$ by plugging in $- \frac{3}{2}$ for $t$ .

$(2 {(- \frac{3}{2})}^{5} - 3 {(lim_{t \to - \frac{3}{2}} t)}^{4} + 5 {(lim_{t \to - \frac{3}{2}} t)}^{3}) \cdot ({(lim_{t \to - \frac{3}{2}} t)}^{4} - {(lim_{t \to - \frac{3}{2}} t)}^{2})$

Step 12.2

Evaluate the limit of $t$ by plugging in $- \frac{3}{2}$ for $t$ .

$(2 {(- \frac{3}{2})}^{5} - 3 {(- \frac{3}{2})}^{4} + 5 {(lim_{t \to - \frac{3}{2}} t)}^{3}) \cdot ({(lim_{t \to - \frac{3}{2}} t)}^{4} - {(lim_{t \to - \frac{3}{2}} t)}^{2})$

Step 12.3

Evaluate the limit of $t$ by plugging in $- \frac{3}{2}$ for $t$ .

$(2 {(- \frac{3}{2})}^{5} - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(lim_{t \to - \frac{3}{2}} t)}^{4} - {(lim_{t \to - \frac{3}{2}} t)}^{2})$

Step 12.4

Evaluate the limit of $t$ by plugging in $- \frac{3}{2}$ for $t$ .

$(2 {(- \frac{3}{2})}^{5} - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(lim_{t \to - \frac{3}{2}} t)}^{2})$

Step 12.5

Evaluate the limit of $t$ by plugging in $- \frac{3}{2}$ for $t$ .

$(2 {(- \frac{3}{2})}^{5} - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13

Simplify the answer.

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Step 13.1

Simplify each term.

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Step 13.1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 13.1.1.1

Apply the product rule to $- \frac{3}{2}$ .

$(2 ({(- 1)}^{5} {(\frac{3}{2})}^{5}) - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.1.2

Apply the product rule to $\frac{3}{2}$ .

$(2 ({(- 1)}^{5} \frac{3^{5}}{2^{5}}) - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.2

Raise $- 1$ to the power of $5$ .

$(2 (- \frac{3^{5}}{2^{5}}) - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.3

Cancel the common factor of $2$ .

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Step 13.1.3.1

Move the leading negative in $- \frac{3^{5}}{2^{5}}$ into the numerator.

$(2 \frac{- 3^{5}}{2^{5}} - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.3.2

Factor $2$ out of $2^{5}$ .

$(2 \frac{- 3^{5}}{2 \cdot 2^{4}} - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.3.3

Cancel the common factor.

$(2 \frac{- 3^{5}}{2 \cdot 2^{4}} - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.3.4

Rewrite the expression.

$(\frac{- 3^{5}}{2^{4}} - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.4

Raise $3$ to the power of $5$ .

$(\frac{- 1 \cdot 243}{2^{4}} - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.5

Raise $2$ to the power of $4$ .

$(\frac{- 1 \cdot 243}{16} - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.6

Multiply $- 1$ by $243$ .

$(\frac{- 243}{16} - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.7

Move the negative in front of the fraction.

$(- \frac{243}{16} - 3 {(- \frac{3}{2})}^{4} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.8

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 13.1.8.1

Apply the product rule to $- \frac{3}{2}$ .

$(- \frac{243}{16} - 3 ({(- 1)}^{4} {(\frac{3}{2})}^{4}) + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.8.2

Apply the product rule to $\frac{3}{2}$ .

$(- \frac{243}{16} - 3 ({(- 1)}^{4} \frac{3^{4}}{2^{4}}) + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.9

Raise $- 1$ to the power of $4$ .

$(- \frac{243}{16} - 3 (1 \frac{3^{4}}{2^{4}}) + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.10

Multiply $\frac{3^{4}}{2^{4}}$ by $1$ .

$(- \frac{243}{16} - 3 \frac{3^{4}}{2^{4}} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.11

Raise $3$ to the power of $4$ .

$(- \frac{243}{16} - 3 \frac{81}{2^{4}} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.12

Raise $2$ to the power of $4$ .

$(- \frac{243}{16} - 3 (\frac{81}{16}) + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.13

Multiply $- 3 (\frac{81}{16})$ .

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Step 13.1.13.1

Combine $- 3$ and $\frac{81}{16}$ .

$(- \frac{243}{16} + \frac{- 3 \cdot 81}{16} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.13.2

Multiply $- 3$ by $81$ .

$(- \frac{243}{16} + \frac{- 243}{16} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.14

Move the negative in front of the fraction.

$(- \frac{243}{16} - \frac{243}{16} + 5 {(- \frac{3}{2})}^{3}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.15

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 13.1.15.1

Apply the product rule to $- \frac{3}{2}$ .

$(- \frac{243}{16} - \frac{243}{16} + 5 ({(- 1)}^{3} {(\frac{3}{2})}^{3})) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.15.2

Apply the product rule to $\frac{3}{2}$ .

$(- \frac{243}{16} - \frac{243}{16} + 5 ({(- 1)}^{3} \frac{3^{3}}{2^{3}})) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.16

Raise $- 1$ to the power of $3$ .

$(- \frac{243}{16} - \frac{243}{16} + 5 (- \frac{3^{3}}{2^{3}})) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.17

Raise $3$ to the power of $3$ .

$(- \frac{243}{16} - \frac{243}{16} + 5 (- \frac{27}{2^{3}})) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.18

Raise $2$ to the power of $3$ .

$(- \frac{243}{16} - \frac{243}{16} + 5 (- \frac{27}{8})) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.19

Multiply $5 (- \frac{27}{8})$ .

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Step 13.1.19.1

Multiply $- 1$ by $5$ .

$(- \frac{243}{16} - \frac{243}{16} - 5 (\frac{27}{8})) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.19.2

Combine $- 5$ and $\frac{27}{8}$ .

$(- \frac{243}{16} - \frac{243}{16} + \frac{- 5 \cdot 27}{8}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.19.3

Multiply $- 5$ by $27$ .

$(- \frac{243}{16} - \frac{243}{16} + \frac{- 135}{8}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.1.20

Move the negative in front of the fraction.

$(- \frac{243}{16} - \frac{243}{16} - \frac{135}{8}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.2

Combine the numerators over the common denominator.

$(\frac{- 243 - 243}{16} + \frac{- 135}{8}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.3

Subtract $243$ from $- 243$ .

$(\frac{- 486}{16} + \frac{- 135}{8}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.4

Simplify each term.

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Step 13.4.1

Cancel the common factor of $- 486$ and $16$ .

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Step 13.4.1.1

Factor $2$ out of $- 486$ .

$(\frac{2 (- 243)}{16} + \frac{- 135}{8}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.4.1.2

Cancel the common factors.

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Step 13.4.1.2.1

Factor $2$ out of $16$ .

$(\frac{2 \cdot - 243}{2 \cdot 8} + \frac{- 135}{8}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.4.1.2.2

Cancel the common factor.

$(\frac{2 \cdot - 243}{2 \cdot 8} + \frac{- 135}{8}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.4.1.2.3

Rewrite the expression.

$(\frac{- 243}{8} + \frac{- 135}{8}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.4.2

Move the negative in front of the fraction.

$(- \frac{243}{8} + \frac{- 135}{8}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.4.3

Move the negative in front of the fraction.

$(- \frac{243}{8} - \frac{135}{8}) \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.5

Combine the numerators over the common denominator.

$\frac{- 243 - 135}{8} \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.6

Subtract $135$ from $- 243$ .

$\frac{- 378}{8} \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.7

Cancel the common factor of $- 378$ and $8$ .

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Step 13.7.1

Factor $2$ out of $- 378$ .

$\frac{2 (- 189)}{8} \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.7.2

Cancel the common factors.

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Step 13.7.2.1

Factor $2$ out of $8$ .

$\frac{2 \cdot - 189}{2 \cdot 4} \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.7.2.2

Cancel the common factor.

$\frac{2 \cdot - 189}{2 \cdot 4} \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.7.2.3

Rewrite the expression.

$\frac{- 189}{4} \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.8

Move the negative in front of the fraction.

$- \frac{189}{4} \cdot ({(- \frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.9

Simplify each term.

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Step 13.9.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 13.9.1.1

Apply the product rule to $- \frac{3}{2}$ .

$- \frac{189}{4} \cdot ({(- 1)}^{4} {(\frac{3}{2})}^{4} - {(- \frac{3}{2})}^{2})$

Step 13.9.1.2

Apply the product rule to $\frac{3}{2}$ .

$- \frac{189}{4} \cdot ({(- 1)}^{4} \frac{3^{4}}{2^{4}} - {(- \frac{3}{2})}^{2})$

Step 13.9.2

Raise $- 1$ to the power of $4$ .

$- \frac{189}{4} \cdot (1 \frac{3^{4}}{2^{4}} - {(- \frac{3}{2})}^{2})$

Step 13.9.3

Multiply $\frac{3^{4}}{2^{4}}$ by $1$ .

$- \frac{189}{4} \cdot (\frac{3^{4}}{2^{4}} - {(- \frac{3}{2})}^{2})$

Step 13.9.4

Raise $3$ to the power of $4$ .

$- \frac{189}{4} \cdot (\frac{81}{2^{4}} - {(- \frac{3}{2})}^{2})$

Step 13.9.5

Raise $2$ to the power of $4$ .

$- \frac{189}{4} \cdot (\frac{81}{16} - {(- \frac{3}{2})}^{2})$

Step 13.9.6

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 13.9.6.1

Apply the product rule to $- \frac{3}{2}$ .

$- \frac{189}{4} \cdot (\frac{81}{16} - ({(- 1)}^{2} {(\frac{3}{2})}^{2}))$

Step 13.9.6.2

Apply the product rule to $\frac{3}{2}$ .

$- \frac{189}{4} \cdot (\frac{81}{16} - ({(- 1)}^{2} \frac{3^{2}}{2^{2}}))$

Step 13.9.7

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 13.9.7.1

Move ${(- 1)}^{2}$ .

$- \frac{189}{4} \cdot (\frac{81}{16} + {(- 1)}^{2} \cdot - 1 \frac{3^{2}}{2^{2}})$

Step 13.9.7.2

Multiply ${(- 1)}^{2}$ by $- 1$ .

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Step 13.9.7.2.1

Raise $- 1$ to the power of $1$ .

$- \frac{189}{4} \cdot (\frac{81}{16} + {(- 1)}^{2} \cdot {(- 1)}^{1} \frac{3^{2}}{2^{2}})$

Step 13.9.7.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{189}{4} \cdot (\frac{81}{16} + {(- 1)}^{2 + 1} \frac{3^{2}}{2^{2}})$

Step 13.9.7.3

Add $2$ and $1$ .

$- \frac{189}{4} \cdot (\frac{81}{16} + {(- 1)}^{3} \frac{3^{2}}{2^{2}})$

Step 13.9.8

Raise $- 1$ to the power of $3$ .

$- \frac{189}{4} \cdot (\frac{81}{16} - \frac{3^{2}}{2^{2}})$

Step 13.9.9

Raise $3$ to the power of $2$ .

$- \frac{189}{4} \cdot (\frac{81}{16} - \frac{9}{2^{2}})$

Step 13.9.10

Raise $2$ to the power of $2$ .

$- \frac{189}{4} \cdot (\frac{81}{16} - \frac{9}{4})$

Step 13.10

To write $- \frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{189}{4} \cdot (\frac{81}{16} - \frac{9}{4} \cdot \frac{4}{4})$

Step 13.11

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 13.11.1

Multiply $\frac{9}{4}$ by $\frac{4}{4}$ .

$- \frac{189}{4} \cdot (\frac{81}{16} - \frac{9 \cdot 4}{4 \cdot 4})$

Step 13.11.2

Multiply $4$ by $4$ .

$- \frac{189}{4} \cdot (\frac{81}{16} - \frac{9 \cdot 4}{16})$

Step 13.12

Combine the numerators over the common denominator.

$- \frac{189}{4} \cdot \frac{81 - 9 \cdot 4}{16}$

Step 13.13

Simplify the numerator.

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Step 13.13.1

Multiply $- 9$ by $4$ .

$- \frac{189}{4} \cdot \frac{81 - 36}{16}$

Step 13.13.2

Subtract $36$ from $81$ .

$- \frac{189}{4} \cdot \frac{45}{16}$

Step 13.14

Multiply $- \frac{189}{4} \cdot \frac{45}{16}$ .

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Step 13.14.1

Multiply $\frac{45}{16}$ by $\frac{189}{4}$ .

$- \frac{45 \cdot 189}{16 \cdot 4}$

Step 13.14.2

Multiply $45$ by $189$ .

$- \frac{8505}{16 \cdot 4}$

Step 13.14.3

Multiply $16$ by $4$ .

$- \frac{8505}{64}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$- \frac{8505}{64}$

Decimal Form:

$- 132.890625$