Algebra Examples

$\frac{2 {(a^{2})}^{3}}{- 10 a^{- 8}}$

Step 1

Move $a^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{2 {(a^{2})}^{3} a^{8}}{- 10}$

Step 2

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

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Step 2.1

Factor $2$ out of $2 {(a^{2})}^{3} a^{8}$ .

$\frac{2 ({(a^{2})}^{3} a^{8})}{- 10}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $- 10$ .

$\frac{2 ({(a^{2})}^{3} a^{8})}{2 \cdot - 5}$

Step 2.2.2

Cancel the common factor.

$\frac{2 ({(a^{2})}^{3} a^{8})}{2 \cdot - 5}$

Step 2.2.3

Rewrite the expression.

$\frac{{(a^{2})}^{3} a^{8}}{- 5}$

Step 3

Multiply the exponents in ${(a^{2})}^{3}$ .

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Step 3.1

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

$\frac{a^{2 \cdot 3} a^{8}}{- 5}$

Step 3.2

Multiply $2$ by $3$ .

$\frac{a^{6} a^{8}}{- 5}$

Step 4

Multiply $a^{6}$ by $a^{8}$ by adding the exponents.

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Step 4.1

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

$\frac{a^{6 + 8}}{- 5}$

Step 4.2

Add $6$ and $8$ .

$\frac{a^{14}}{- 5}$

Step 5

Move the negative in front of the fraction.

$- \frac{a^{14}}{5}$