Precalculus Examples

${(\frac{a^{6} y}{y^{4}})}^{\frac{5}{2}}$

Step 1

Cancel the common factor of $y$ and $y^{4}$ .

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Step 1.1

Factor $y$ out of $a^{6} y$ .

${(\frac{y a^{6}}{y^{4}})}^{\frac{5}{2}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $y$ out of $y^{4}$ .

${(\frac{y a^{6}}{y \cdot y^{3}})}^{\frac{5}{2}}$

Step 1.2.2

Cancel the common factor.

${(\frac{y a^{6}}{y \cdot y^{3}})}^{\frac{5}{2}}$

Step 1.2.3

Rewrite the expression.

${(\frac{a^{6}}{y^{3}})}^{\frac{5}{2}}$

Step 2

Apply basic rules of exponents.

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Step 2.1

Apply the product rule to $\frac{a^{6}}{y^{3}}$ .

$\frac{{(a^{6})}^{\frac{5}{2}}}{{(y^{3})}^{\frac{5}{2}}}$

Step 2.2

Multiply the exponents in ${(a^{6})}^{\frac{5}{2}}$ .

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Step 2.2.1

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

$\frac{a^{6 (\frac{5}{2})}}{{(y^{3})}^{\frac{5}{2}}}$

Step 2.2.2

Cancel the common factor of $2$ .

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Step 2.2.2.1

Factor $2$ out of $6$ .

$\frac{a^{2 (3) \frac{5}{2}}}{{(y^{3})}^{\frac{5}{2}}}$

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

Step 2.2.3

Multiply $3$ by $5$ .

$\frac{a^{15}}{{(y^{3})}^{\frac{5}{2}}}$

Step 2.3

Multiply the exponents in ${(y^{3})}^{\frac{5}{2}}$ .

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Step 2.3.1

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

$\frac{a^{15}}{y^{3 (\frac{5}{2})}}$

Step 2.3.2

Multiply $3 (\frac{5}{2})$ .

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Step 2.3.2.1

Combine $3$ and $\frac{5}{2}$ .

$\frac{a^{15}}{y^{\frac{3 \cdot 5}{2}}}$

Step 2.3.2.2

Multiply $3$ by $5$ .

$\frac{a^{15}}{y^{\frac{15}{2}}}$