Evaluate (16/25)^(1/2)

${(\frac{16}{25})}^{\frac{1}{2}}$

Step 1

Apply the product rule to $\frac{16}{25}$ .

$\frac{16^{\frac{1}{2}}}{25^{\frac{1}{2}}}$

Step 2

Simplify the numerator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 3

Simplify the denominator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{4}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$