Finite Math Examples

${(\frac{9 x^{- 2}}{16 y^{4}})}^{\frac{1}{2}}$

Step 1

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{9}{16 y^{4} x^{2}})}^{\frac{1}{2}}$

Step 2

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

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Step 2.1

Apply the product rule to $\frac{9}{16 y^{4} x^{2}}$ .

$\frac{9^{\frac{1}{2}}}{{(16 y^{4} x^{2})}^{\frac{1}{2}}}$

Step 2.2

Apply the product rule to $16 y^{4} x^{2}$ .

$\frac{9^{\frac{1}{2}}}{{(16 y^{4})}^{\frac{1}{2}} {(x^{2})}^{\frac{1}{2}}}$

Step 2.3

Apply the product rule to $16 y^{4}$ .

$\frac{9^{\frac{1}{2}}}{16^{\frac{1}{2}} {(y^{4})}^{\frac{1}{2}} {(x^{2})}^{\frac{1}{2}}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $9$ as $3^{2}$ .

$\frac{{(3^{2})}^{\frac{1}{2}}}{16^{\frac{1}{2}} {(y^{4})}^{\frac{1}{2}} {(x^{2})}^{\frac{1}{2}}}$

Step 3.2

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

$\frac{3^{2 (\frac{1}{2})}}{16^{\frac{1}{2}} {(y^{4})}^{\frac{1}{2}} {(x^{2})}^{\frac{1}{2}}}$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

$\frac{3^{2 (\frac{1}{2})}}{16^{\frac{1}{2}} {(y^{4})}^{\frac{1}{2}} {(x^{2})}^{\frac{1}{2}}}$

Step 3.3.2

Rewrite the expression.

$\frac{3^{1}}{16^{\frac{1}{2}} {(y^{4})}^{\frac{1}{2}} {(x^{2})}^{\frac{1}{2}}}$

Step 3.4

Evaluate the exponent.

$\frac{3}{16^{\frac{1}{2}} {(y^{4})}^{\frac{1}{2}} {(x^{2})}^{\frac{1}{2}}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $16$ as $4^{2}$ .

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

Step 4.2

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

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

Step 4.3

Cancel the common factor of $2$ .

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Step 4.3.1

Cancel the common factor.

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

Step 4.3.2

Rewrite the expression.

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

Step 4.4

Evaluate the exponent.

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

Step 4.5

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

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Step 4.5.1

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

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

Step 4.5.2

Cancel the common factor of $2$ .

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Step 4.5.2.1

Factor $2$ out of $4$ .

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

Step 4.5.2.2

Cancel the common factor.

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

Step 4.5.2.3

Rewrite the expression.

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

Step 4.6

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

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Step 4.6.1

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

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

Step 4.6.2

Cancel the common factor of $2$ .

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Step 4.6.2.1

Cancel the common factor.

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

Step 4.6.2.2

Rewrite the expression.

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

Step 4.7

Simplify.

$\frac{3}{4 y^{2} x}$