Simplify (a^3b^3c)/(a^-3b^-3c^-1)

$\frac{a^{3} b^{3} c}{a^{- 3} b^{- 3} c^{- 1}}$

Step 1

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

$\frac{a^{3} b^{3} c a^{3}}{b^{- 3} c^{- 1}}$

Step 2

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

$\frac{a^{3} b^{3} c a^{3} b^{3}}{c^{- 1}}$

Step 3

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

$a^{3} b^{3} c a^{3} b^{3} c$

Step 4

Multiply $a^{3}$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

$a^{3} a^{3} b^{3} c b^{3} c$

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

$a^{3 + 3} b^{3} c b^{3} c$

Add $3$ and $3$ .

$a^{6} b^{3} c b^{3} c$

Step 5

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

Move $b^{3}$ .

$a^{6} (b^{3} b^{3}) c \cdot c$

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

$a^{6} b^{3 + 3} c \cdot c$

Add $3$ and $3$ .

$a^{6} b^{6} c \cdot c$

Step 6

Multiply $c$ by $c$ by adding the exponents.

Move $c$ .

$a^{6} b^{6} (c \cdot c)$

Multiply $c$ by $c$ .

$a^{6} b^{6} c^{2}$