Basic Math Examples

$(6 m^{- 2} n^{8}) (- 9 m^{- 5} n^{7})$

Step 1

Multiply $m^{- 2}$ by $m^{- 5}$ by adding the exponents.

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Step 1.1

Move $m^{- 5}$ .

$6 (m^{- 5} m^{- 2}) n^{8} (- 9 n^{7})$

Step 1.2

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

$6 m^{- 5 - 2} n^{8} (- 9 n^{7})$

Step 1.3

Subtract $2$ from $- 5$ .

$6 m^{- 7} n^{8} (- 9 n^{7})$

Step 2

Multiply $n^{8}$ by $n^{7}$ by adding the exponents.

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Step 2.1

Move $n^{7}$ .

$6 m^{- 7} (n^{7} n^{8}) \cdot - 9$

Step 2.2

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

$6 m^{- 7} n^{7 + 8} \cdot - 9$

Step 2.3

Add $7$ and $8$ .

$6 m^{- 7} n^{15} \cdot - 9$

Step 3

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

$6 \frac{1}{m^{7}} n^{15} \cdot - 9$

Step 4

Combine $6$ and $\frac{1}{m^{7}}$ .

$\frac{6}{m^{7}} n^{15} \cdot - 9$

Step 5

Combine $\frac{6}{m^{7}}$ and $n^{15}$ .

$\frac{6 n^{15}}{m^{7}} \cdot - 9$

Step 6

Multiply $\frac{6 n^{15}}{m^{7}} \cdot - 9$ .

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Step 6.1

Combine $\frac{6 n^{15}}{m^{7}}$ and $- 9$ .

$\frac{6 n^{15} \cdot - 9}{m^{7}}$

Step 6.2

Multiply $- 9$ by $6$ .

$\frac{- 54 n^{15}}{m^{7}}$

Step 7

Move the negative in front of the fraction.

$- \frac{54 n^{15}}{m^{7}}$