Evaluate (25/64)^(3/2)

${(\frac{25}{64})}^{\frac{3}{2}}$

Step 1

Apply the product rule to $\frac{25}{64}$ .

$\frac{25^{\frac{3}{2}}}{64^{\frac{3}{2}}}$

Step 2

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$\frac{{(5^{2})}^{\frac{3}{2}}}{64^{\frac{3}{2}}}$

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

$\frac{5^{2 (\frac{3}{2})}}{64^{\frac{3}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5^{2 (\frac{3}{2})}}{64^{\frac{3}{2}}}$

Rewrite the expression.

$\frac{5^{3}}{64^{\frac{3}{2}}}$

Raise $5$ to the power of $3$ .

$\frac{125}{64^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

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

$\frac{125}{{(8^{2})}^{\frac{3}{2}}}$

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

$\frac{125}{8^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{125}{8^{2 (\frac{3}{2})}}$

Rewrite the expression.

$\frac{125}{8^{3}}$

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

$\frac{125}{512}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{125}{512}$

Decimal Form:

$0.24414062 \dots$