Simplify (a^2a^3(a^-1))^2

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

Step 1

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

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

${(a^{2 + 3} \cdot a^{- 1})}^{2}$

Add $2$ and $3$ .

${(a^{5} \cdot a^{- 1})}^{2}$

Step 2

Multiply $a^{5}$ by $a^{- 1}$ by adding the exponents.

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

${(a^{5 - 1})}^{2}$

Subtract $1$ from $5$ .

${(a^{4})}^{2}$

Step 3

Multiply the exponents in ${(a^{4})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$a^{4 \cdot 2}$

Multiply $4$ by $2$ .

$a^{8}$

Simplify (a^2*a^3*(a^-1))^2