Simplify (a^-2b^8)/(a^5b^-2c^3)

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

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.

Move $a^{2}$ .

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

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

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

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.

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

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

Add $8$ and $2$ .

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