Algebra Examples

$\frac{{(3 m^{2})}^{2} {(- 4 n^{5})}^{2}}{8 m^{3} n^{4}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $3 m^{2}$ .

$\frac{3^{2} {(m^{2})}^{2} {(- 4 n^{5})}^{2}}{8 m^{3} n^{4}}$

Step 1.2

Apply the product rule to $- 4 n^{5}$ .

$\frac{3^{2} {(m^{2})}^{2} {(- 4)}^{2} {(n^{5})}^{2}}{8 m^{3} n^{4}}$

Step 1.3

Raise $3$ to the power of $2$ .

$\frac{9 {(m^{2})}^{2} {(- 4)}^{2} {(n^{5})}^{2}}{8 m^{3} n^{4}}$

Step 1.4

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

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Step 1.4.1

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

$\frac{9 m^{2 \cdot 2} {(- 4)}^{2} {(n^{5})}^{2}}{8 m^{3} n^{4}}$

Step 1.4.2

Multiply $2$ by $2$ .

$\frac{9 m^{4} {(- 4)}^{2} {(n^{5})}^{2}}{8 m^{3} n^{4}}$

Step 1.5

Raise $- 4$ to the power of $2$ .

$\frac{9 m^{4} \cdot 16 {(n^{5})}^{2}}{8 m^{3} n^{4}}$

Step 1.6

Multiply the exponents in ${(n^{5})}^{2}$ .

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Step 1.6.1

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

$\frac{9 m^{4} \cdot 16 n^{5 \cdot 2}}{8 m^{3} n^{4}}$

Step 1.6.2

Multiply $5$ by $2$ .

$\frac{9 m^{4} \cdot 16 n^{10}}{8 m^{3} n^{4}}$

Step 1.7

Multiply $16$ by $9$ .

$\frac{144 m^{4} n^{10}}{8 m^{3} n^{4}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $144$ and $8$ .

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Step 2.1.1

Factor $8$ out of $144 m^{4} n^{10}$ .

$\frac{8 (18 m^{4} n^{10})}{8 m^{3} n^{4}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $8$ out of $8 m^{3} n^{4}$ .

$\frac{8 (18 m^{4} n^{10})}{8 (m^{3} n^{4})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{8 (18 m^{4} n^{10})}{8 (m^{3} n^{4})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{18 m^{4} n^{10}}{m^{3} n^{4}}$

Step 2.2

Cancel the common factor of $m^{4}$ and $m^{3}$ .

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Step 2.2.1

Factor $m^{3}$ out of $18 m^{4} n^{10}$ .

$\frac{m^{3} (18 m n^{10})}{m^{3} n^{4}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $m^{3}$ out of $m^{3} n^{4}$ .

$\frac{m^{3} (18 m n^{10})}{m^{3} (n^{4})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{m^{3} (18 m n^{10})}{m^{3} n^{4}}$

Step 2.2.2.3

Rewrite the expression.

$\frac{18 m n^{10}}{n^{4}}$

Step 2.3

Cancel the common factor of $n^{10}$ and $n^{4}$ .

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Step 2.3.1

Factor $n^{4}$ out of $18 m n^{10}$ .

$\frac{n^{4} (18 m n^{6})}{n^{4}}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Multiply by $1$ .

$\frac{n^{4} (18 m n^{6})}{n^{4} \cdot 1}$

Step 2.3.2.2

Cancel the common factor.

$\frac{n^{4} (18 m n^{6})}{n^{4} \cdot 1}$

Step 2.3.2.3

Rewrite the expression.

$\frac{18 m n^{6}}{1}$

Step 2.3.2.4

Divide $18 m n^{6}$ by $1$ .

$18 m n^{6}$