Write the Fraction in Simplest Form (12a^8)/((3a^-1)^-1)

$\frac{12 a^{8}}{{(3 a^{- 1})}^{- 1}}$

Step 1

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

$12 a^{8} (3 a^{- 1})$

Step 2

Multiply $a^{8}$ by $a^{- 1}$ by adding the exponents.

Move $a^{- 1}$ .

$12 (a^{- 1} a^{8}) \cdot 3$

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

$12 a^{- 1 + 8} \cdot 3$

Add $- 1$ and $8$ .

$12 a^{7} \cdot 3$

Step 3

Multiply $3$ by $12$ .

$36 a^{7}$