Algebra Examples

$\frac{{(4 {(6 - 3)}^{2} - 5 ({(- 1)}^{2} + 7))}^{3} - 5}{- 3^{2} (2 + 3) + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Simplify each term.

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Step 1.1.1

Subtract $3$ from $6$ .

$\frac{{(4 \cdot 3^{2} - 5 ({(- 1)}^{2} + 7))}^{3} - 5}{- 3^{2} (2 + 3) + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 1.1.2

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

$\frac{{(4 \cdot 9 - 5 ({(- 1)}^{2} + 7))}^{3} - 5}{- 3^{2} (2 + 3) + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 1.1.3

Multiply $4$ by $9$ .

$\frac{{(36 - 5 ({(- 1)}^{2} + 7))}^{3} - 5}{- 3^{2} (2 + 3) + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 1.1.4

Raise $- 1$ to the power of $2$ .

$\frac{{(36 - 5 (1 + 7))}^{3} - 5}{- 3^{2} (2 + 3) + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 1.1.5

Add $1$ and $7$ .

$\frac{{(36 - 5 \cdot 8)}^{3} - 5}{- 3^{2} (2 + 3) + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 1.1.6

Multiply $- 5$ by $8$ .

$\frac{{(36 - 40)}^{3} - 5}{- 3^{2} (2 + 3) + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 1.2

Subtract $40$ from $36$ .

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

Step 1.3

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

$\frac{- 64 - 5}{- 3^{2} (2 + 3) + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 1.4

Subtract $5$ from $- 64$ .

$\frac{- 69}{- 3^{2} (2 + 3) + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{- 69}{- 1 \cdot 9 (2 + 3) + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 2.2

Multiply $- 1$ by $9$ .

$\frac{- 69}{- 9 (2 + 3) + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 2.3

Add $2$ and $3$ .

$\frac{- 69}{- 9 \cdot 5 + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 2.4

Multiply $- 9$ by $5$ .

$\frac{- 69}{- 45 + 3 {(- 2)}^{2} - {(- 1)}^{3} {(- 3)}^{2}}$

Step 2.5

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

$\frac{- 69}{- 45 + 3 \cdot 4 - {(- 1)}^{3} {(- 3)}^{2}}$

Step 2.6

Multiply $3$ by $4$ .

$\frac{- 69}{- 45 + 12 - {(- 1)}^{3} {(- 3)}^{2}}$

Step 2.7

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

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Step 2.7.1

Multiply $- 1$ by ${(- 1)}^{3}$ .

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Step 2.7.1.1

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

$\frac{- 69}{- 45 + 12 + {(- 1)}^{1} {(- 1)}^{3} {(- 3)}^{2}}$

Step 2.7.1.2

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

$\frac{- 69}{- 45 + 12 + {(- 1)}^{1 + 3} {(- 3)}^{2}}$

Step 2.7.2

Add $1$ and $3$ .

$\frac{- 69}{- 45 + 12 + {(- 1)}^{4} {(- 3)}^{2}}$

Step 2.8

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

$\frac{- 69}{- 45 + 12 + 1 {(- 3)}^{2}}$

Step 2.9

Multiply ${(- 3)}^{2}$ by $1$ .

$\frac{- 69}{- 45 + 12 + {(- 3)}^{2}}$

Step 2.10

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

$\frac{- 69}{- 45 + 12 + 9}$

Step 2.11

Add $- 45$ and $12$ .

$\frac{- 69}{- 33 + 9}$

Step 2.12

Add $- 33$ and $9$ .

$\frac{- 69}{- 24}$

Step 3

Cancel the common factor of $- 69$ and $- 24$ .

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Step 3.1

Factor $- 3$ out of $- 69$ .

$\frac{- 3 (23)}{- 24}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $- 3$ out of $- 24$ .

$\frac{- 3 \cdot 23}{- 3 \cdot 8}$

Step 3.2.2

Cancel the common factor.

$\frac{- 3 \cdot 23}{- 3 \cdot 8}$

Step 3.2.3

Rewrite the expression.

$\frac{23}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{8}$

Decimal Form:

$2.875$

Mixed Number Form:

$2 \frac{7}{8}$