Evaluate (25/36)^(1/2)

${(\frac{25}{36})}^{\frac{1}{2}}$

Step 1

Apply the product rule to $\frac{25}{36}$ .

$\frac{25^{\frac{1}{2}}}{36^{\frac{1}{2}}}$

Step 2

Simplify the numerator.

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

$\frac{{(5^{2})}^{\frac{1}{2}}}{36^{\frac{1}{2}}}$

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

$\frac{5^{2 (\frac{1}{2})}}{36^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5^{2 (\frac{1}{2})}}{36^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{5^{1}}{36^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{5}{36^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

Rewrite $36$ as $6^{2}$ .

$\frac{5}{{(6^{2})}^{\frac{1}{2}}}$

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

$\frac{5}{6^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5}{6^{2 (\frac{1}{2})}}$

Rewrite the expression.

$\frac{5}{6^{1}}$

Evaluate the exponent.

$\frac{5}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{6}$

Decimal Form:

$0.8\overline{3}$