Algebra Examples

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

Step 1

Move $x^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Move $y^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 4

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

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

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, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 5.2

Cancel the common factor of $2$ .

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Step 5.2.1

Factor $2$ out of $4$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 6.2

Cancel the common factor of $2$ .

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Step 6.2.1

Factor $2$ out of $6$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$\frac{x^{2}}{y^{3}}$