Algebra Examples

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

Step 1

Move $m^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Cancel the common factor of $15$ and $3$ .

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Step 2.1

Factor $3$ out of $15$ .

$\frac{3 \cdot 5}{3 {(m^{- 2})}^{4} m^{7}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $3 {(m^{- 2})}^{4} m^{7}$ .

$\frac{3 \cdot 5}{3 ({(m^{- 2})}^{4} m^{7})}$

Step 2.2.2

Cancel the common factor.

$\frac{3 \cdot 5}{3 ({(m^{- 2})}^{4} m^{7})}$

Step 2.2.3

Rewrite the expression.

$\frac{5}{{(m^{- 2})}^{4} m^{7}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply the exponents in ${(m^{- 2})}^{4}$ .

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Step 3.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{5}{m^{- 2 \cdot 4} m^{7}}$

Step 3.1.2

Multiply $- 2$ by $4$ .

$\frac{5}{m^{- 8} m^{7}}$

Step 3.2

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

$\frac{5}{\frac{1}{m^{8}} m^{7}}$

Step 4

Combine $\frac{1}{m^{8}}$ and $m^{7}$ .

$\frac{5}{\frac{m^{7}}{m^{8}}}$

Step 5

Reduce the expression $\frac{m^{7}}{m^{8}}$ by cancelling the common factors.

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Step 5.1

Multiply by $1$ .

$\frac{5}{\frac{m^{7} \cdot 1}{m^{8}}}$

Step 5.2

Factor $m^{7}$ out of $m^{8}$ .

$\frac{5}{\frac{m^{7} \cdot 1}{m^{7} m}}$

Step 5.3

Cancel the common factor.

$\frac{5}{\frac{m^{7} \cdot 1}{m^{7} m}}$

Step 5.4

Rewrite the expression.

$\frac{5}{\frac{1}{m}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$5 m$