Simplify ((5^2)/(8^2))^(-1/2)

${(\frac{5^{2}}{8^{2}})}^{- \frac{1}{2}}$

Raise $5$ to the power of $2$ .

${(\frac{25}{8^{2}})}^{- \frac{1}{2}}$

Raise $8$ to the power of $2$ .

${(\frac{25}{64})}^{- \frac{1}{2}}$

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

${(\frac{64}{25})}^{\frac{1}{2}}$

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

$\frac{64^{\frac{1}{2}}}{25^{\frac{1}{2}}}$

Simplify the numerator.

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

$\frac{{(8^{2})}^{\frac{1}{2}}}{25^{\frac{1}{2}}}$

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

$\frac{8^{2 (\frac{1}{2})}}{25^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{8^{2 (\frac{1}{2})}}{25^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{8^{1}}{25^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{8}{25^{\frac{1}{2}}}$

Simplify the denominator.

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

$\frac{8}{{(5^{2})}^{\frac{1}{2}}}$

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

$\frac{8}{5^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{8}{5^{2 (\frac{1}{2})}}$

Rewrite the expression.

$\frac{8}{5^{1}}$

Evaluate the exponent.

$\frac{8}{5}$

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{5}$

Decimal Form:

$1.6$

Mixed Number Form:

$1 \frac{3}{5}$