Simplify ((y^2)/25)^(1/2)

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

Apply the product rule to $\frac{y^{2}}{25}$ .

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

Simplify the numerator.

Multiply the exponents in ${(y^{2})}^{\frac{1}{2}}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the denominator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{y}{5}$