Basic Math Examples

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

Step 1

Cancel the common factor of $w^{5}$ and $w^{3}$ .

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Step 1.1

Factor $w^{3}$ out of $w^{5}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $w^{3}$ out of $2 w^{3}$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

${(\frac{w^{2}}{2})}^{5}$

Step 2

Simplify the expression.

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Step 2.1

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

$\frac{{(w^{2})}^{5}}{2^{5}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{w^{2 \cdot 5}}{2^{5}}$

Step 2.2.2

Multiply $2$ by $5$ .

$\frac{w^{10}}{2^{5}}$

Step 2.3

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

$\frac{w^{10}}{32}$