Basic Math Examples

$m^{- 2} n^{6} \cdot (m^{3} n^{- 8})$

Step 1

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

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Step 1.1

Move $m^{3}$ .

$m^{3} m^{- 2} n^{6} \cdot n^{- 8}$

Step 1.2

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

$m^{3 - 2} n^{6} \cdot n^{- 8}$

Step 1.3

Subtract $2$ from $3$ .

$m^{1} n^{6} \cdot n^{- 8}$

Step 2

Simplify $m^{1} n^{6} \cdot n^{- 8}$ .

$m n^{6} \cdot n^{- 8}$

Step 3

Multiply $n^{6}$ by $n^{- 8}$ by adding the exponents.

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Step 3.1

Move $n^{- 8}$ .

$m (n^{- 8} n^{6})$

Step 3.2

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

$m n^{- 8 + 6}$

Step 3.3

Add $- 8$ and $6$ .

$m n^{- 2}$

Step 4

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

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

Step 5

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

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