Algebra Examples

$\frac{4 t^{9} s}{{(2 t^{4} s^{- 3})}^{- 3}}$

Step 1

Move ${(2 t^{4} s^{- 3})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4 t^{9} s {(2 t^{4} s^{- 3})}^{3}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$4 t^{9} s {(2 t^{4} \frac{1}{s^{3}})}^{3}$

Step 3

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

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Step 3.1

Combine $2$ and $\frac{1}{s^{3}}$ .

$4 t^{9} s {(t^{4} \frac{2}{s^{3}})}^{3}$

Step 3.2

Combine $t^{4}$ and $\frac{2}{s^{3}}$ .

$4 t^{9} s {(\frac{t^{4} \cdot 2}{s^{3}})}^{3}$

Step 4

Move $2$ to the left of $t^{4}$ .

$4 t^{9} s {(\frac{2 \cdot t^{4}}{s^{3}})}^{3}$

Step 5

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

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Step 5.1

Apply the product rule to $\frac{2 t^{4}}{s^{3}}$ .

$4 t^{9} s \frac{{(2 t^{4})}^{3}}{{(s^{3})}^{3}}$

Step 5.2

Apply the product rule to $2 t^{4}$ .

$4 t^{9} s \frac{2^{3} {(t^{4})}^{3}}{{(s^{3})}^{3}}$

Step 6

Simplify the numerator.

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Step 6.1

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

$4 t^{9} s \frac{8 {(t^{4})}^{3}}{{(s^{3})}^{3}}$

Step 6.2

Multiply the exponents in ${(t^{4})}^{3}$ .

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Step 6.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 t^{9} s \frac{8 t^{4 \cdot 3}}{{(s^{3})}^{3}}$

Step 6.2.2

Multiply $4$ by $3$ .

$4 t^{9} s \frac{8 t^{12}}{{(s^{3})}^{3}}$

Step 7

Simplify terms.

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Step 7.1

Multiply the exponents in ${(s^{3})}^{3}$ .

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Step 7.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 t^{9} s \frac{8 t^{12}}{s^{3 \cdot 3}}$

Step 7.1.2

Multiply $3$ by $3$ .

$4 t^{9} s \frac{8 t^{12}}{s^{9}}$

Step 7.2

Cancel the common factor of $s$ .

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Step 7.2.1

Factor $s$ out of $4 t^{9} s$ .

$s (4 t^{9}) \frac{8 t^{12}}{s^{9}}$

Step 7.2.2

Factor $s$ out of $s^{9}$ .

$s (4 t^{9}) \frac{8 t^{12}}{s \cdot s^{8}}$

Step 7.2.3

Cancel the common factor.

$s (4 t^{9}) \frac{8 t^{12}}{s \cdot s^{8}}$

Step 7.2.4

Rewrite the expression.

$4 t^{9} \frac{8 t^{12}}{s^{8}}$

Step 7.3

Combine $4$ and $\frac{8 t^{12}}{s^{8}}$ .

$t^{9} \frac{4 (8 t^{12})}{s^{8}}$

Step 7.4

Multiply $8$ by $4$ .

$t^{9} \frac{32 t^{12}}{s^{8}}$

Step 7.5

Combine $t^{9}$ and $\frac{32 t^{12}}{s^{8}}$ .

$\frac{t^{9} (32 t^{12})}{s^{8}}$

Step 8

Multiply $t^{9}$ by $t^{12}$ by adding the exponents.

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Step 8.1

Move $t^{12}$ .

$\frac{t^{12} t^{9} \cdot 32}{s^{8}}$

Step 8.2

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

$\frac{t^{12 + 9} \cdot 32}{s^{8}}$

Step 8.3

Add $12$ and $9$ .

$\frac{t^{21} \cdot 32}{s^{8}}$

Step 9

Move $32$ to the left of $t^{21}$ .

$\frac{32 t^{21}}{s^{8}}$