Algebra Examples

$m n^{2} \cdot m^{2} n^{- 4} \cdot m n^{- 1}$

Step 1

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

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Step 1.1

Move $m^{2}$ .

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

Step 1.2

Multiply $m^{2}$ by $m$ .

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.3

Add $2$ and $1$ .

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

Step 2

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

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Step 2.1

Move $m$ .

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

Step 2.2

Multiply $m$ by $m^{3}$ .

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Step 2.2.1

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

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

Step 2.2.2

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

$m^{1 + 3} n^{2} \cdot n^{- 4} \cdot n^{- 1}$

Step 2.3

Add $1$ and $3$ .

$m^{4} n^{2} \cdot n^{- 4} \cdot n^{- 1}$

Step 3

Multiply $n^{2}$ by $n^{- 4}$ by adding the exponents.

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Step 3.1

Move $n^{- 4}$ .

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

Step 3.2

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

$m^{4} n^{- 4 + 2} \cdot n^{- 1}$

Step 3.3

Add $- 4$ and $2$ .

$m^{4} n^{- 2} \cdot n^{- 1}$

Step 4

Multiply $n^{- 2}$ by $n^{- 1}$ by adding the exponents.

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Step 4.1

Move $n^{- 1}$ .

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

Step 4.2

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

$m^{4} n^{- 1 - 2}$

Step 4.3

Subtract $2$ from $- 1$ .

$m^{4} n^{- 3}$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$m^{4} \frac{1}{n^{3}}$

Step 6

Combine $m^{4}$ and $\frac{1}{n^{3}}$ .

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