Calculus Examples

${(x^{30} y^{15})}^{\frac{1}{5}}$

Step 1

Apply the product rule to $x^{30} y^{15}$ .

${(x^{30})}^{\frac{1}{5}} {(y^{15})}^{\frac{1}{5}}$

Step 2

Multiply the exponents in ${(x^{30})}^{\frac{1}{5}}$ .

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Step 2.1

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

$x^{30 (\frac{1}{5})} {(y^{15})}^{\frac{1}{5}}$

Step 2.2

Cancel the common factor of $5$ .

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Step 2.2.1

Factor $5$ out of $30$ .

$x^{5 (6) \frac{1}{5}} {(y^{15})}^{\frac{1}{5}}$

Step 2.2.2

Cancel the common factor.

$x^{5 \cdot 6 \frac{1}{5}} {(y^{15})}^{\frac{1}{5}}$

Step 2.2.3

Rewrite the expression.

$x^{6} {(y^{15})}^{\frac{1}{5}}$

Step 3

Multiply the exponents in ${(y^{15})}^{\frac{1}{5}}$ .

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Step 3.1

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

$x^{6} y^{15 (\frac{1}{5})}$

Step 3.2

Cancel the common factor of $5$ .

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Step 3.2.1

Factor $5$ out of $15$ .

$x^{6} y^{5 (3) \frac{1}{5}}$

Step 3.2.2

Cancel the common factor.

$x^{6} y^{5 \cdot 3 \frac{1}{5}}$

Step 3.2.3

Rewrite the expression.

$x^{6} y^{3}$