Finite Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $6$ .

$\frac{y^{2 (3) \frac{1}{2}}}{{(x^{4})}^{\frac{1}{2}}}$

Step 3.2.2

Cancel the common factor.

$\frac{y^{2 \cdot 3 \frac{1}{2}}}{{(x^{4})}^{\frac{1}{2}}}$

Step 3.2.3

Rewrite the expression.

$\frac{y^{3}}{{(x^{4})}^{\frac{1}{2}}}$

Step 4

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

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Step 4.1

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

$\frac{y^{3}}{x^{4 (\frac{1}{2})}}$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Factor $2$ out of $4$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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