Precalculus Examples

${(8 w^{2} z^{- 2})}^{2} (z^{3})$

Step 1

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

${(8 w^{2} \frac{1}{z^{2}})}^{2} z^{3}$

Step 2

Multiply $8 w^{2} \frac{1}{z^{2}}$ .

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Step 2.1

Combine $8$ and $\frac{1}{z^{2}}$ .

${(w^{2} \frac{8}{z^{2}})}^{2} z^{3}$

Step 2.2

Combine $w^{2}$ and $\frac{8}{z^{2}}$ .

${(\frac{w^{2} \cdot 8}{z^{2}})}^{2} z^{3}$

Step 3

Move $8$ to the left of $w^{2}$ .

${(\frac{8 \cdot w^{2}}{z^{2}})}^{2} z^{3}$

Step 4

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

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Step 4.1

Apply the product rule to $\frac{8 w^{2}}{z^{2}}$ .

$\frac{{(8 w^{2})}^{2}}{{(z^{2})}^{2}} z^{3}$

Step 4.2

Apply the product rule to $8 w^{2}$ .

$\frac{8^{2} {(w^{2})}^{2}}{{(z^{2})}^{2}} z^{3}$

Step 5

Simplify the numerator.

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Step 5.1

Raise $8$ to the power of $2$ .

$\frac{64 {(w^{2})}^{2}}{{(z^{2})}^{2}} z^{3}$

Step 5.2

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

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Step 5.2.1

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

$\frac{64 w^{2 \cdot 2}}{{(z^{2})}^{2}} z^{3}$

Step 5.2.2

Multiply $2$ by $2$ .

$\frac{64 w^{4}}{{(z^{2})}^{2}} z^{3}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

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

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Step 6.1.1

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

$\frac{64 w^{4}}{z^{2 \cdot 2}} z^{3}$

Step 6.1.2

Multiply $2$ by $2$ .

$\frac{64 w^{4}}{z^{4}} z^{3}$

Step 6.2

Cancel the common factor of $z^{3}$ .

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Step 6.2.1

Factor $z^{3}$ out of $z^{4}$ .

$\frac{64 w^{4}}{z^{3} z} z^{3}$

Step 6.2.2

Cancel the common factor.

$\frac{64 w^{4}}{z^{3} z} z^{3}$

Step 6.2.3

Rewrite the expression.

$\frac{64 w^{4}}{z}$