Algebra Examples

${(\frac{3 m^{2} n^{7}}{m n^{3}})}^{5}$

Step 1

Cancel the common factor of $m^{2}$ and $m$ .

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Step 1.1

Factor $m$ out of $3 m^{2} n^{7}$ .

${(\frac{m (3 m n^{7})}{m n^{3}})}^{5}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $m$ out of $m n^{3}$ .

${(\frac{m (3 m n^{7})}{m (n^{3})})}^{5}$

Step 1.2.2

Cancel the common factor.

${(\frac{m (3 m n^{7})}{m n^{3}})}^{5}$

Step 1.2.3

Rewrite the expression.

${(\frac{3 m n^{7}}{n^{3}})}^{5}$

Step 2

Cancel the common factor of $n^{7}$ and $n^{3}$ .

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Step 2.1

Factor $n^{3}$ out of $3 m n^{7}$ .

${(\frac{n^{3} (3 m n^{4})}{n^{3}})}^{5}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

${(\frac{n^{3} (3 m n^{4})}{n^{3} \cdot 1})}^{5}$

Step 2.2.2

Cancel the common factor.

${(\frac{n^{3} (3 m n^{4})}{n^{3} \cdot 1})}^{5}$

Step 2.2.3

Rewrite the expression.

${(\frac{3 m n^{4}}{1})}^{5}$

Step 2.2.4

Divide $3 m n^{4}$ by $1$ .

${(3 m n^{4})}^{5}$

Step 3

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

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Step 3.1

Apply the product rule to $3 m n^{4}$ .

${(3 m)}^{5} {(n^{4})}^{5}$

Step 3.2

Apply the product rule to $3 m$ .

$3^{5} m^{5} {(n^{4})}^{5}$

Step 4

Raise $3$ to the power of $5$ .

$243 m^{5} {(n^{4})}^{5}$

Step 5

Multiply the exponents in ${(n^{4})}^{5}$ .

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Step 5.1

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

$243 m^{5} n^{4 \cdot 5}$

Step 5.2

Multiply $4$ by $5$ .

$243 m^{5} n^{20}$