Simplify (24a^-7b^-2c)/(6a^-2b^-3c^-6)

$\frac{24 a^{- 7} b^{- 2} c}{6 a^{- 2} b^{- 3} c^{- 6}}$

Move $a^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{24 b^{- 2} c}{6 a^{- 2} b^{- 3} c^{- 6} a^{7}}$

Multiply $a^{- 2}$ by $a^{7}$ by adding the exponents.

Move $a^{7}$ .

$\frac{24 b^{- 2} c}{6 (a^{7} a^{- 2}) b^{- 3} c^{- 6}}$

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

$\frac{24 b^{- 2} c}{6 a^{7 - 2} b^{- 3} c^{- 6}}$

Subtract $2$ from $7$ .

$\frac{24 b^{- 2} c}{6 a^{5} b^{- 3} c^{- 6}}$

Move $b^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{24 b^{- 2} c b^{3}}{6 a^{5} c^{- 6}}$

Move $c^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{24 b^{- 2} c b^{3} c^{6}}{6 a^{5}}$

Simplify the numerator.

Multiply $b^{- 2}$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

$\frac{24 (b^{3} b^{- 2}) c \cdot c^{6}}{6 a^{5}}$

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

$\frac{24 b^{3 - 2} c \cdot c^{6}}{6 a^{5}}$

Subtract $2$ from $3$ .

$\frac{24 b^{1} c \cdot c^{6}}{6 a^{5}}$

Simplify $24 b^{1} c$ .

$\frac{24 b c \cdot c^{6}}{6 a^{5}}$

Multiply $c$ by $c^{6}$ by adding the exponents.

Move $c^{6}$ .

$\frac{24 b (c^{6} c)}{6 a^{5}}$

Multiply $c^{6}$ by $c$ .

Raise $c$ to the power of $1$ .

$\frac{24 b (c^{6} c^{1})}{6 a^{5}}$

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

$\frac{24 b c^{6 + 1}}{6 a^{5}}$

Add $6$ and $1$ .

$\frac{24 b c^{7}}{6 a^{5}}$

Cancel the common factor of $24$ and $6$ .

Factor $6$ out of $24 b c^{7}$ .

$\frac{6 (4 b c^{7})}{6 a^{5}}$

Cancel the common factors.

Factor $6$ out of $6 a^{5}$ .

$\frac{6 (4 b c^{7})}{6 (a^{5})}$

Cancel the common factor.

$\frac{6 (4 b c^{7})}{6 a^{5}}$

Rewrite the expression.

$\frac{4 b c^{7}}{a^{5}}$