Find the Exact Value (4/25)^(-1/2)

${(\frac{4}{25})}^{- \frac{1}{2}}$

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

${(\frac{25}{4})}^{\frac{1}{2}}$

Apply the product rule to $\frac{25}{4}$ .

$\frac{25^{\frac{1}{2}}}{4^{\frac{1}{2}}}$

Simplify the numerator.

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

$\frac{{(5^{2})}^{\frac{1}{2}}}{4^{\frac{1}{2}}}$

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

$\frac{5^{2 (\frac{1}{2})}}{4^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5^{2 (\frac{1}{2})}}{4^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{5^{1}}{4^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{5}{4^{\frac{1}{2}}}$

Simplify the denominator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$