Pre-Algebra Examples

${(\frac{16}{9})}^{\frac{- 3}{2}}$

Step 1

Move the negative in front of the fraction.

${(\frac{16}{9})}^{- \frac{3}{2}}$

Step 2

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

${(\frac{9}{16})}^{\frac{3}{2}}$

Step 3

Apply the product rule to $\frac{9}{16}$ .

$\frac{9^{\frac{3}{2}}}{16^{\frac{3}{2}}}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{{(3^{2})}^{\frac{3}{2}}}{16^{\frac{3}{2}}}$

Step 4.2

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

$\frac{3^{2 (\frac{3}{2})}}{16^{\frac{3}{2}}}$

Step 4.3

Cancel the common factor of $2$ .

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Step 4.3.1

Cancel the common factor.

$\frac{3^{2 (\frac{3}{2})}}{16^{\frac{3}{2}}}$

Step 4.3.2

Rewrite the expression.

$\frac{3^{3}}{16^{\frac{3}{2}}}$

Step 4.4

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

$\frac{27}{16^{\frac{3}{2}}}$

Step 5

Simplify the denominator.

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Step 5.1

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

$\frac{27}{{(4^{2})}^{\frac{3}{2}}}$

Step 5.2

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

$\frac{27}{4^{2 (\frac{3}{2})}}$

Step 5.3

Cancel the common factor of $2$ .

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Step 5.3.1

Cancel the common factor.

$\frac{27}{4^{2 (\frac{3}{2})}}$

Step 5.3.2

Rewrite the expression.

$\frac{27}{4^{3}}$

Step 5.4

Raise $4$ to the power of $3$ .

$\frac{27}{64}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{64}$

Decimal Form:

$0.421875$