Algebra Examples

$\frac{2 (n m^{4})}{2 m^{- 1} n^{- 2} \cdot n^{3}}$

Step 1

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

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Step 1.1

Move $n^{3}$ .

$\frac{2 (n m^{4})}{2 m^{- 1} (n^{3} n^{- 2})}$

Step 1.2

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

$\frac{2 (n m^{4})}{2 m^{- 1} n^{3 - 2}}$

Step 1.3

Subtract $2$ from $3$ .

$\frac{2 (n m^{4})}{2 m^{- 1} n^{1}}$

Step 2

Simplify $2 m^{- 1} n^{1}$ .

$\frac{2 (n m^{4})}{2 m^{- 1} n}$

Step 3

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

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

Step 4

Multiply $m^{4}$ by $m$ by adding the exponents.

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Step 4.1

Move $m$ .

$\frac{2 (n (m \cdot m^{4}))}{2 n}$

Step 4.2

Multiply $m$ by $m^{4}$ .

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Step 4.2.1

Raise $m$ to the power of $1$ .

$\frac{2 (n (m^{1} m^{4}))}{2 n}$

Step 4.2.2

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

$\frac{2 (n m^{1 + 4})}{2 n}$

Step 4.3

Add $1$ and $4$ .

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

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\frac{n m^{5}}{n}$

Step 6

Cancel the common factor of $n$ .

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Step 6.1

Cancel the common factor.

$\frac{n m^{5}}{n}$

Step 6.2

Divide $m^{5}$ by $1$ .

$m^{5}$