Precalculus Examples

${(\frac{s^{2} t^{- 4}}{5 s^{- 1} t})}^{- 2}$

Step 1

Move $t^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{s^{2}}{5 s^{- 1} t \cdot t^{4}})}^{- 2}$

Step 2

Multiply $t$ by $t^{4}$ by adding the exponents.

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Step 2.1

Move $t^{4}$ .

${(\frac{s^{2}}{5 s^{- 1} (t^{4} t)})}^{- 2}$

Step 2.2

Multiply $t^{4}$ by $t$ .

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Step 2.2.1

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

${(\frac{s^{2}}{5 s^{- 1} (t^{4} t^{1})})}^{- 2}$

Step 2.2.2

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

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

Step 2.3

Add $4$ and $1$ .

${(\frac{s^{2}}{5 s^{- 1} t^{5}})}^{- 2}$

Step 3

Move $s^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{s^{2} s}{5 t^{5}})}^{- 2}$

Step 4

Multiply $s^{2}$ by $s$ by adding the exponents.

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Step 4.1

Multiply $s^{2}$ by $s$ .

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Step 4.1.1

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

${(\frac{s^{2} s^{1}}{5 t^{5}})}^{- 2}$

Step 4.1.2

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

${(\frac{s^{2 + 1}}{5 t^{5}})}^{- 2}$

Step 4.2

Add $2$ and $1$ .

${(\frac{s^{3}}{5 t^{5}})}^{- 2}$

Step 5

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{5 t^{5}}{s^{3}})}^{2}$

Step 6

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

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Step 6.1

Apply the product rule to $\frac{5 t^{5}}{s^{3}}$ .

$\frac{{(5 t^{5})}^{2}}{{(s^{3})}^{2}}$

Step 6.2

Apply the product rule to $5 t^{5}$ .

$\frac{5^{2} {(t^{5})}^{2}}{{(s^{3})}^{2}}$

Step 7

Simplify the numerator.

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Step 7.1

Raise $5$ to the power of $2$ .

$\frac{25 {(t^{5})}^{2}}{{(s^{3})}^{2}}$

Step 7.2

Multiply the exponents in ${(t^{5})}^{2}$ .

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Step 7.2.1

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

$\frac{25 t^{5 \cdot 2}}{{(s^{3})}^{2}}$

Step 7.2.2

Multiply $5$ by $2$ .

$\frac{25 t^{10}}{{(s^{3})}^{2}}$

Step 8

Multiply the exponents in ${(s^{3})}^{2}$ .

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Step 8.1

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

$\frac{25 t^{10}}{s^{3 \cdot 2}}$

Step 8.2

Multiply $3$ by $2$ .

$\frac{25 t^{10}}{s^{6}}$