Algebra Examples

$\frac{2 {(a^{- 1})}^{3}}{- 10 a^{5}}$

Step 1

Cancel the common factor of $2$ and $- 10$ .

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Step 1.1

Factor $2$ out of $2 {(a^{- 1})}^{3}$ .

$\frac{2 ({(a^{- 1})}^{3})}{- 10 a^{5}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $- 10 a^{5}$ .

$\frac{2 ({(a^{- 1})}^{3})}{2 (- 5 a^{5})}$

Step 1.2.2

Cancel the common factor.

$\frac{2 {(a^{- 1})}^{3}}{2 (- 5 a^{5})}$

Step 1.2.3

Rewrite the expression.

$\frac{{(a^{- 1})}^{3}}{- 5 a^{5}}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply the exponents in ${(a^{- 1})}^{3}$ .

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Step 2.1.1

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

$\frac{a^{- 1 \cdot 3}}{- 5 a^{5}}$

Step 2.1.2

Multiply $- 1$ by $3$ .

$\frac{a^{- 3}}{- 5 a^{5}}$

Step 2.2

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

$\frac{\frac{1}{a^{3}}}{- 5 a^{5}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{a^{3}} \cdot \frac{1}{- 5 a^{5}}$

Step 4

Combine.

$\frac{1 \cdot 1}{a^{3} (- 5 a^{5})}$

Step 5

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

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Step 5.1

Move $a^{5}$ .

$\frac{1 \cdot 1}{a^{5} a^{3} \cdot - 5}$

Step 5.2

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

$\frac{1 \cdot 1}{a^{5 + 3} \cdot - 5}$

Step 5.3

Add $5$ and $3$ .

$\frac{1 \cdot 1}{a^{8} \cdot - 5}$

Step 6

Multiply $1$ by $1$ .

$\frac{1}{a^{8} \cdot - 5}$

Step 7

Move $- 5$ to the left of $a^{8}$ .

$\frac{1}{- 5 \cdot a^{8}}$

Step 8

Move the negative in front of the fraction.

$- \frac{1}{5 a^{8}}$