Simplify (n/(m^2p^4))^(1/2)

${(\frac{n}{m^{2} p^{4}})}^{\frac{1}{2}}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{n}{m^{2} p^{4}}$ .

$\frac{n^{\frac{1}{2}}}{{(m^{2} p^{4})}^{\frac{1}{2}}}$

Apply the product rule to $m^{2} p^{4}$ .

$\frac{n^{\frac{1}{2}}}{{(m^{2})}^{\frac{1}{2}} {(p^{4})}^{\frac{1}{2}}}$

Simplify the denominator.

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

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

$\frac{n^{\frac{1}{2}}}{m^{2 (\frac{1}{2})} {(p^{4})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{n^{\frac{1}{2}}}{m^{2 (\frac{1}{2})} {(p^{4})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{n^{\frac{1}{2}}}{m^{1} {(p^{4})}^{\frac{1}{2}}}$

Simplify.

$\frac{n^{\frac{1}{2}}}{m {(p^{4})}^{\frac{1}{2}}}$

Multiply the exponents in ${(p^{4})}^{\frac{1}{2}}$ .

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

$\frac{n^{\frac{1}{2}}}{m p^{4 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{n^{\frac{1}{2}}}{m p^{2 (2) \frac{1}{2}}}$

Cancel the common factor.

$\frac{n^{\frac{1}{2}}}{m p^{2 \cdot 2 \frac{1}{2}}}$

Rewrite the expression.

$\frac{n^{\frac{1}{2}}}{m p^{2}}$