Precalculus Examples

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

Step 1

Apply the product rule to $x^{2} y^{4}$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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

Step 3

Simplify.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Factor $2$ out of $4$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$x y^{2}$