Basic Math Examples

$2 m^{- 3} n^{4} \cdot (2 m^{- 5} n^{- 5})$

Step 1

Multiply $m^{- 3}$ by $m^{- 5}$ by adding the exponents.

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Step 1.1

Move $m^{- 5}$ .

$2 (m^{- 5} m^{- 3}) n^{4} \cdot (2 n^{- 5})$

Step 1.2

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

$2 m^{- 5 - 3} n^{4} \cdot (2 n^{- 5})$

Step 1.3

Subtract $3$ from $- 5$ .

$2 m^{- 8} n^{4} \cdot (2 n^{- 5})$

Step 2

Multiply $n^{4}$ by $n^{- 5}$ by adding the exponents.

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Step 2.1

Move $n^{- 5}$ .

$2 m^{- 8} (n^{- 5} n^{4}) \cdot 2$

Step 2.2

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

$2 m^{- 8} n^{- 5 + 4} \cdot 2$

Step 2.3

Add $- 5$ and $4$ .

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

Step 3

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

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

Step 4

Combine $2$ and $\frac{1}{m^{8}}$ .

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

Step 5

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

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

Step 6

Combine.

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

Step 7

Multiply $2$ by $1$ .

$\frac{2}{m^{8} n} \cdot 2$

Step 8

Multiply $\frac{2}{m^{8} n} \cdot 2$ .

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Step 8.1

Combine $\frac{2}{m^{8} n}$ and $2$ .

$\frac{2 \cdot 2}{m^{8} n}$

Step 8.2

Multiply $2$ by $2$ .

$\frac{4}{m^{8} n}$