Algebra Examples

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

Step 1

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

$\frac{m^{2} p}{m n^{3} p^{- 2} n}$

Step 2

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

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Step 2.1

Move $n$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

$\frac{m^{2} p}{m n^{1 + 3} p^{- 2}}$

Step 2.3

Add $1$ and $3$ .

$\frac{m^{2} p}{m n^{4} p^{- 2}}$

Step 3

Move $p^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{m^{2} p \cdot p^{2}}{m n^{4}}$

Step 4

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

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Step 4.1

Move $p^{2}$ .

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.3

Add $2$ and $1$ .

$\frac{m^{2} p^{3}}{m n^{4}}$

Step 5

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

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Step 5.1

Factor $m$ out of $m^{2} p^{3}$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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