Basic Math Examples

$\frac{8}{9^{- \frac{3}{2}}}$

Step 1

Move $9^{- \frac{3}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$8 \cdot 9^{\frac{3}{2}}$

Step 2

Simplify the expression.

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Step 2.1

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

$8 \cdot {(3^{2})}^{\frac{3}{2}}$

Step 2.2

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

$8 \cdot 3^{2 (\frac{3}{2})}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$8 \cdot 3^{2 (\frac{3}{2})}$

Step 3.2

Rewrite the expression.

$8 \cdot 3^{3}$

Step 4

Simplify the expression.

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Step 4.1

Raise $3$ to the power of $3$ .

$8 \cdot 27$

Step 4.2

Multiply $8$ by $27$ .

$216$