Precalculus Examples

${(25 x^{4} y^{6})}^{\frac{1}{2}}$

Step 1

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

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Step 1.1

Apply the product rule to $25 x^{4} y^{6}$ .

${(25 x^{4})}^{\frac{1}{2}} {(y^{6})}^{\frac{1}{2}}$

Step 1.2

Apply the product rule to $25 x^{4}$ .

$25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}} {(y^{6})}^{\frac{1}{2}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $25$ as $5^{2}$ .

${(5^{2})}^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}} {(y^{6})}^{\frac{1}{2}}$

Step 2.2

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

$5^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}} {(y^{6})}^{\frac{1}{2}}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$5^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}} {(y^{6})}^{\frac{1}{2}}$

Step 3.2

Rewrite the expression.

$5^{1} {(x^{4})}^{\frac{1}{2}} {(y^{6})}^{\frac{1}{2}}$

Step 4

Evaluate the exponent.

$5 {(x^{4})}^{\frac{1}{2}} {(y^{6})}^{\frac{1}{2}}$

Step 5

Multiply the exponents in ${(x^{4})}^{\frac{1}{2}}$ .

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Step 5.1

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

$5 x^{4 (\frac{1}{2})} {(y^{6})}^{\frac{1}{2}}$

Step 5.2

Cancel the common factor of $2$ .

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Step 5.2.1

Factor $2$ out of $4$ .

$5 x^{2 (2) \frac{1}{2}} {(y^{6})}^{\frac{1}{2}}$

Step 5.2.2

Cancel the common factor.

$5 x^{2 \cdot 2 \frac{1}{2}} {(y^{6})}^{\frac{1}{2}}$

Step 5.2.3

Rewrite the expression.

$5 x^{2} {(y^{6})}^{\frac{1}{2}}$

Step 6

Multiply the exponents in ${(y^{6})}^{\frac{1}{2}}$ .

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Step 6.1

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

$5 x^{2} y^{6 (\frac{1}{2})}$

Step 6.2

Cancel the common factor of $2$ .

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Step 6.2.1

Factor $2$ out of $6$ .

$5 x^{2} y^{2 (3) \frac{1}{2}}$

Step 6.2.2

Cancel the common factor.

$5 x^{2} y^{2 \cdot 3 \frac{1}{2}}$

Step 6.2.3

Rewrite the expression.

$5 x^{2} y^{3}$