Write the Fraction in Simplest Form ((3a^5r^2)^-1)/(2a^-5r^-2)

$\frac{{(3 a^{5} r^{2})}^{- 1}}{2 a^{- 5} r^{- 2}}$

Step 1

Move ${(3 a^{5} r^{2})}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{2 a^{- 5} r^{- 2} (3 a^{5} r^{2})}$

Step 2

Simplify the denominator.

Multiply $a^{- 5}$ by $a^{5}$ by adding the exponents.

Move $a^{5}$ .

$\frac{1}{2 (a^{5} a^{- 5}) r^{- 2} (3 r^{2})}$

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

$\frac{1}{2 a^{5 - 5} r^{- 2} (3 r^{2})}$

Subtract $5$ from $5$ .

$\frac{1}{2 a^{0} r^{- 2} (3 r^{2})}$

Simplify $2 a^{0} r^{- 2} (3 r^{2})$ .

$\frac{1}{2 r^{- 2} (3 r^{2})}$

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

Move $r^{2}$ .

$\frac{1}{2 (r^{2} r^{- 2}) \cdot 3}$

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

$\frac{1}{2 r^{2 - 2} \cdot 3}$

Subtract $2$ from $2$ .

$\frac{1}{2 r^{0} \cdot 3}$

Simplify $2 r^{0} \cdot 3$ .

$\frac{1}{2 \cdot 3}$

Step 3

Multiply $2$ by $3$ .

$\frac{1}{6}$