Evaluate (9/64)^(3/2)

${(\frac{9}{64})}^{\frac{3}{2}}$

Step 1

Apply the product rule to $\frac{9}{64}$ .

$\frac{9^{\frac{3}{2}}}{64^{\frac{3}{2}}}$

Step 2

Simplify the numerator.

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

$\frac{{(3^{2})}^{\frac{3}{2}}}{64^{\frac{3}{2}}}$

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

$\frac{3^{2 (\frac{3}{2})}}{64^{\frac{3}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3^{2 (\frac{3}{2})}}{64^{\frac{3}{2}}}$

Rewrite the expression.

$\frac{3^{3}}{64^{\frac{3}{2}}}$

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

$\frac{27}{64^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

Rewrite $64$ as $8^{2}$ .

$\frac{27}{{(8^{2})}^{\frac{3}{2}}}$

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

$\frac{27}{8^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{27}{8^{2 (\frac{3}{2})}}$

Rewrite the expression.

$\frac{27}{8^{3}}$

Raise $8$ to the power of $3$ .

$\frac{27}{512}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{512}$

Decimal Form:

$0.05273437 \dots$