Pre-Algebra Examples

${(\frac{1}{4} \cdot (w^{5} z^{3}))}^{2}$

Step 1

Multiply $\frac{1}{4} (w^{5} z^{3})$ .

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Step 1.1

Combine $w^{5}$ and $\frac{1}{4}$ .

${(\frac{w^{5}}{4} z^{3})}^{2}$

Step 1.2

Combine $\frac{w^{5}}{4}$ and $z^{3}$ .

${(\frac{w^{5} z^{3}}{4})}^{2}$

Step 2

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

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Step 2.1

Apply the product rule to $\frac{w^{5} z^{3}}{4}$ .

$\frac{{(w^{5} z^{3})}^{2}}{4^{2}}$

Step 2.2

Apply the product rule to $w^{5} z^{3}$ .

$\frac{{(w^{5})}^{2} {(z^{3})}^{2}}{4^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

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

$\frac{w^{5 \cdot 2} {(z^{3})}^{2}}{4^{2}}$

Step 3.1.2

Multiply $5$ by $2$ .

$\frac{w^{10} {(z^{3})}^{2}}{4^{2}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{w^{10} z^{3 \cdot 2}}{4^{2}}$

Step 3.2.2

Multiply $3$ by $2$ .

$\frac{w^{10} z^{6}}{4^{2}}$

Step 4

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

$\frac{w^{10} z^{6}}{16}$