Simplify ((4m^8y^12)/(8p^20))^(1/4)

${(\frac{4 m^{8} y^{12}}{8 p^{20}})}^{\frac{1}{4}}$

Step 1

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4 m^{8} y^{12}$ .

${(\frac{4 (m^{8} y^{12})}{8 p^{20}})}^{\frac{1}{4}}$

Cancel the common factors.

Factor $4$ out of $8 p^{20}$ .

${(\frac{4 (m^{8} y^{12})}{4 (2 p^{20})})}^{\frac{1}{4}}$

Cancel the common factor.

${(\frac{4 (m^{8} y^{12})}{4 (2 p^{20})})}^{\frac{1}{4}}$

Rewrite the expression.

${(\frac{m^{8} y^{12}}{2 p^{20}})}^{\frac{1}{4}}$

Step 2

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

Apply the product rule to $\frac{m^{8} y^{12}}{2 p^{20}}$ .

$\frac{{(m^{8} y^{12})}^{\frac{1}{4}}}{{(2 p^{20})}^{\frac{1}{4}}}$

Apply the product rule to $m^{8} y^{12}$ .

$\frac{{(m^{8})}^{\frac{1}{4}} {(y^{12})}^{\frac{1}{4}}}{{(2 p^{20})}^{\frac{1}{4}}}$

Apply the product rule to $2 p^{20}$ .

$\frac{{(m^{8})}^{\frac{1}{4}} {(y^{12})}^{\frac{1}{4}}}{2^{\frac{1}{4}} {(p^{20})}^{\frac{1}{4}}}$

Step 3

Simplify the numerator.

Multiply the exponents in ${(m^{8})}^{\frac{1}{4}}$ .

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

$\frac{m^{8 (\frac{1}{4})} {(y^{12})}^{\frac{1}{4}}}{2^{\frac{1}{4}} {(p^{20})}^{\frac{1}{4}}}$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{m^{4 (2) \frac{1}{4}} {(y^{12})}^{\frac{1}{4}}}{2^{\frac{1}{4}} {(p^{20})}^{\frac{1}{4}}}$

Cancel the common factor.

$\frac{m^{4 \cdot 2 \frac{1}{4}} {(y^{12})}^{\frac{1}{4}}}{2^{\frac{1}{4}} {(p^{20})}^{\frac{1}{4}}}$

Rewrite the expression.

$\frac{m^{2} {(y^{12})}^{\frac{1}{4}}}{2^{\frac{1}{4}} {(p^{20})}^{\frac{1}{4}}}$

Multiply the exponents in ${(y^{12})}^{\frac{1}{4}}$ .

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

$\frac{m^{2} y^{12 (\frac{1}{4})}}{2^{\frac{1}{4}} {(p^{20})}^{\frac{1}{4}}}$

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$\frac{m^{2} y^{4 (3) \frac{1}{4}}}{2^{\frac{1}{4}} {(p^{20})}^{\frac{1}{4}}}$

Cancel the common factor.

$\frac{m^{2} y^{4 \cdot 3 \frac{1}{4}}}{2^{\frac{1}{4}} {(p^{20})}^{\frac{1}{4}}}$

Rewrite the expression.

$\frac{m^{2} y^{3}}{2^{\frac{1}{4}} {(p^{20})}^{\frac{1}{4}}}$

Step 4

Simplify the expression.

Multiply the exponents in ${(p^{20})}^{\frac{1}{4}}$ .

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

$\frac{m^{2} y^{3}}{2^{\frac{1}{4}} p^{20 (\frac{1}{4})}}$

Cancel the common factor of $4$ .

Factor $4$ out of $20$ .

$\frac{m^{2} y^{3}}{2^{\frac{1}{4}} p^{4 (5) \frac{1}{4}}}$

Cancel the common factor.

$\frac{m^{2} y^{3}}{2^{\frac{1}{4}} p^{4 \cdot 5 \frac{1}{4}}}$

Rewrite the expression.

$\frac{m^{2} y^{3}}{2^{\frac{1}{4}} p^{5}}$

Reorder factors in $\frac{m^{2} y^{3}}{2^{\frac{1}{4}} p^{5}}$ .

$\frac{m^{2} y^{3}}{p^{5} \cdot 2^{\frac{1}{4}}}$

Simplify ((4m^8y^12)/(8p^20))^(1/4)

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