Evaluate (16/25)^(-3/2)

${(\frac{16}{25})}^{- \frac{3}{2}}$

Step 1

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

${(\frac{25}{16})}^{\frac{3}{2}}$

Step 2

Apply the product rule to $\frac{25}{16}$ .

$\frac{25^{\frac{3}{2}}}{16^{\frac{3}{2}}}$

Step 3

Simplify the numerator.

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

$\frac{{(5^{2})}^{\frac{3}{2}}}{16^{\frac{3}{2}}}$

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

$\frac{5^{2 (\frac{3}{2})}}{16^{\frac{3}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5^{2 (\frac{3}{2})}}{16^{\frac{3}{2}}}$

Rewrite the expression.

$\frac{5^{3}}{16^{\frac{3}{2}}}$

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

$\frac{125}{16^{\frac{3}{2}}}$

Step 4

Simplify the denominator.

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

$\frac{125}{{(4^{2})}^{\frac{3}{2}}}$

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

$\frac{125}{4^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{125}{4^{2 (\frac{3}{2})}}$

Rewrite the expression.

$\frac{125}{4^{3}}$

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

$\frac{125}{64}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{125}{64}$

Decimal Form:

$1.953125$

Mixed Number Form:

$1 \frac{61}{64}$