Precalculus Examples

$\frac{4}{9^{- \frac{1}{2}}}$

Step 1

Move $9^{- \frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4 \cdot 9^{\frac{1}{2}}$

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$4 \cdot 3^{1}$

Step 4

Evaluate the exponent.

$4 \cdot 3$

Step 5

Multiply $4$ by $3$ .

$12$