Algebra Examples

$(8 m^{- 2} n^{4}) (\frac{1}{2} n^{- 2})$

Step 1

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

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Step 1.1

Move $n^{- 2}$ .

$8 m^{- 2} (n^{- 2} n^{4}) \frac{1}{2}$

Step 1.2

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

$8 m^{- 2} n^{- 2 + 4} \frac{1}{2}$

Step 1.3

Add $- 2$ and $4$ .

$8 m^{- 2} n^{2} \frac{1}{2}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $8 m^{- 2} n^{2}$ .

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

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

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

Step 4

Combine $4$ and $\frac{1}{m^{2}}$ .

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

Step 5

Combine $\frac{4}{m^{2}}$ and $n^{2}$ .

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