Simplify (a^6b^7c^7)/(a^-2b^3c^0)

$\frac{a^{6} b^{7} c^{7}}{a^{- 2} b^{3} c^{0}}$

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

$\frac{a^{6} b^{7} c^{7} a^{2}}{b^{3}}$

Move $c^{0}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{a^{6} b^{7} c^{7} a^{2} c^{0}}{b^{3} c^{0}}$

Simplify the numerator.

Multiply $a^{6}$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$\frac{a^{2} a^{6} b^{7} c^{7} c^{0}}{b^{3} c^{0}}$

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

$\frac{a^{2 + 6} b^{7} c^{7} c^{0}}{b^{3} c^{0}}$

Add $2$ and $6$ .

$\frac{a^{8} b^{7} c^{7} c^{0}}{b^{3} c^{0}}$

Multiply $c^{7}$ by $c^{0}$ by adding the exponents.

Move $c^{0}$ .

$\frac{a^{8} b^{7} (c^{0} c^{7})}{b^{3} c^{0}}$

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

$\frac{a^{8} b^{7} c^{0 + 7}}{b^{3} c^{0}}$

Add $0$ and $7$ .

$\frac{a^{8} b^{7} c^{7}}{b^{3} c^{0}}$

Move $c^{0}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{a^{8} b^{7} c^{7} c^{0}}{b^{3}}$

Multiply $c^{7}$ by $c^{0}$ by adding the exponents.

Move $c^{0}$ .

$\frac{a^{8} b^{7} (c^{0} c^{7})}{b^{3}}$

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

$\frac{a^{8} b^{7} c^{0 + 7}}{b^{3}}$

Add $0$ and $7$ .

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

Cancel the common factor of $b^{7}$ and $b^{3}$ .

Factor $b^{3}$ out of $a^{8} b^{7} c^{7}$ .

$\frac{b^{3} (a^{8} b^{4} c^{7})}{b^{3}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{b^{3} (a^{8} b^{4} c^{7})}{b^{3} \cdot 1}$

Cancel the common factor.

$\frac{b^{3} (a^{8} b^{4} c^{7})}{b^{3} \cdot 1}$

Rewrite the expression.

$\frac{a^{8} b^{4} c^{7}}{1}$

Divide $a^{8} b^{4} c^{7}$ by $1$ .

$a^{8} b^{4} c^{7}$