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

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

Step 1

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

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

Step 2

Simplify the numerator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 3

Simplify the denominator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{2}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{5}$

Decimal Form:

$0.4$