Algebra Examples

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

Step 1

Move $a^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

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

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Step 2.1

Move $a^{2}$ .

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

Step 2.2

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

$\frac{b^{8}}{a^{2 + 5} b^{- 2} c^{3}}$

Step 2.3

Add $2$ and $5$ .

$\frac{b^{8}}{a^{7} b^{- 2} c^{3}}$

Step 3

Move $b^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{b^{8} b^{2}}{a^{7} c^{3}}$

Step 4

Multiply $b^{8}$ by $b^{2}$ 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.

$\frac{b^{8 + 2}}{a^{7} c^{3}}$

Step 4.2

Add $8$ and $2$ .

$\frac{b^{10}}{a^{7} c^{3}}$