Algebra Examples

$(7 m n^{2}) (- 15 m^{- 4} n^{3})$

Step 1

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

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Step 1.1

Move $m^{- 4}$ .

$7 (m^{- 4} m) n^{2} (- 15 n^{3})$

Step 1.2

Multiply $m^{- 4}$ by $m$ .

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Step 1.2.1

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

$7 (m^{- 4} m^{1}) n^{2} (- 15 n^{3})$

Step 1.2.2

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

$7 m^{- 4 + 1} n^{2} (- 15 n^{3})$

Step 1.3

Add $- 4$ and $1$ .

$7 m^{- 3} n^{2} (- 15 n^{3})$

Step 2

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

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Step 2.1

Move $n^{3}$ .

$7 m^{- 3} (n^{3} n^{2}) \cdot - 15$

Step 2.2

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

$7 m^{- 3} n^{3 + 2} \cdot - 15$

Step 2.3

Add $3$ and $2$ .

$7 m^{- 3} n^{5} \cdot - 15$

Step 3

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

$7 \frac{1}{m^{3}} n^{5} \cdot - 15$

Step 4

Combine $7$ and $\frac{1}{m^{3}}$ .

$\frac{7}{m^{3}} n^{5} \cdot - 15$

Step 5

Combine $\frac{7}{m^{3}}$ and $n^{5}$ .

$\frac{7 n^{5}}{m^{3}} \cdot - 15$

Step 6

Multiply $\frac{7 n^{5}}{m^{3}} \cdot - 15$ .

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Step 6.1

Combine $\frac{7 n^{5}}{m^{3}}$ and $- 15$ .

$\frac{7 n^{5} \cdot - 15}{m^{3}}$

Step 6.2

Multiply $- 15$ by $7$ .

$\frac{- 105 n^{5}}{m^{3}}$

Step 7

Move the negative in front of the fraction.

$- \frac{105 n^{5}}{m^{3}}$