Algebra Examples

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

Step 1

Move $m^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Multiply $m^{2}$ by $m^{3}$ by adding the exponents.

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Step 2.1

Move $m^{3}$ .

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

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.3

Add $3$ and $2$ .

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $4$ and $2$ .

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Step 3.1.1

Factor $2$ out of $4 m^{5} (3 n^{5})$ .

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

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $2 {(- m n)}^{3}$ .

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

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

Step 3.2

Multiply $3$ by $2$ .

$\frac{6 m^{5} n^{5}}{{(- m n)}^{3}}$

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to $- m n$ .

$\frac{6 m^{5} n^{5}}{{(- m)}^{3} n^{3}}$

Step 4.2

Apply the product rule to $- m$ .

$\frac{6 m^{5} n^{5}}{{(- 1)}^{3} m^{3} n^{3}}$

Step 4.3

Raise $- 1$ to the power of $3$ .

$\frac{6 m^{5} n^{5}}{- m^{3} n^{3}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $m^{5}$ and $m^{3}$ .

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Step 5.1.1

Factor $m^{3}$ out of $6 m^{5} n^{5}$ .

$\frac{m^{3} (6 m^{2} n^{5})}{- m^{3} n^{3}}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

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

$\frac{m^{3} (6 m^{2} n^{5})}{m^{3} (- 1 n^{3})}$

Step 5.1.2.2

Cancel the common factor.

$\frac{m^{3} (6 m^{2} n^{5})}{m^{3} (- 1 n^{3})}$

Step 5.1.2.3

Rewrite the expression.

$\frac{6 m^{2} n^{5}}{- 1 n^{3}}$

Step 5.2

Cancel the common factor of $n^{5}$ and $n^{3}$ .

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Step 5.2.1

Factor $n^{3}$ out of $6 m^{2} n^{5}$ .

$\frac{n^{3} (6 m^{2} n^{2})}{- 1 n^{3}}$

Step 5.2.2

Move the negative one from the denominator of $\frac{6 m^{2} n^{2}}{- 1}$ .

$- 1 \cdot (6 m^{2} n^{2})$

Step 5.3

Simplify the expression.

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Step 5.3.1

Rewrite $- 1 \cdot (6 m^{2} n^{2})$ as $- (6 m^{2} n^{2})$ .

$- (6 m^{2} n^{2})$

Step 5.3.2

Multiply $6$ by $- 1$ .

$- 6 m^{2} n^{2}$