Simplify (25^(-3/2))^(1/3)

${(25^{- \frac{3}{2}})}^{\frac{1}{3}}$

Multiply the exponents in ${(25^{- \frac{3}{2}})}^{\frac{1}{3}}$ .

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

$25^{- \frac{3}{2} \cdot \frac{1}{3}}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$25^{\frac{- 3}{2} \cdot \frac{1}{3}}$

Factor $3$ out of $- 3$ .

$25^{\frac{3 (- 1)}{2} \cdot \frac{1}{3}}$

Cancel the common factor.

$25^{\frac{3 \cdot - 1}{2} \cdot \frac{1}{3}}$

Rewrite the expression.

$25^{\frac{- 1}{2}}$

Move the negative in front of the fraction.

$25^{- \frac{1}{2}}$

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

$\frac{1}{25^{\frac{1}{2}}}$

Simplify the denominator.

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

$\frac{1}{{(5^{2})}^{\frac{1}{2}}}$

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

$\frac{1}{5^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{5^{2 (\frac{1}{2})}}$

Rewrite the expression.

$\frac{1}{5^{1}}$

Evaluate the exponent.

$\frac{1}{5}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$