Evaluate (16^(-3/5))^(5/4)

${(16^{- \frac{3}{5}})}^{\frac{5}{4}}$

Step 1

Multiply the exponents in ${(16^{- \frac{3}{5}})}^{\frac{5}{4}}$ .

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

$16^{- \frac{3}{5} \cdot \frac{5}{4}}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$16^{\frac{- 3}{5} \cdot \frac{5}{4}}$

Cancel the common factor.

$16^{\frac{- 3}{5} \cdot \frac{5}{4}}$

Rewrite the expression.

$16^{- 3 (\frac{1}{4})}$

Combine $- 3$ and $\frac{1}{4}$ .

$16^{\frac{- 3}{4}}$

Move the negative in front of the fraction.

$16^{- \frac{3}{4}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{16^{\frac{3}{4}}}$

Step 3

Simplify the denominator.

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

$\frac{1}{{(2^{4})}^{\frac{3}{4}}}$

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

$\frac{1}{2^{4 (\frac{3}{4})}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{1}{2^{4 (\frac{3}{4})}}$

Rewrite the expression.

$\frac{1}{2^{3}}$

Raise $2$ to the power of $3$ .

$\frac{1}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$