Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

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.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

Cancel the common factor of $4$ .

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Step 3.1.2.1

Factor $4$ out of $8$ .

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor of $4$ .

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Step 3.2.2.1

Factor $4$ out of $12$ .

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

Step 3.2.2.2

Cancel the common factor.

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

Step 3.2.2.3

Rewrite the expression.

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

Step 4

Simplify the expression.

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

Cancel the common factor of $4$ .

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Step 4.1.2.1

Factor $4$ out of $20$ .

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

Step 4.1.2.2

Cancel the common factor.

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

Step 4.1.2.3

Rewrite the expression.

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

Step 4.2

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

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