Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Add $2$ and $3$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Subtract $1$ from $5$ .

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

Step 3

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

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Step 3.1

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

$a^{4 \cdot 2}$

Step 3.2

Multiply $4$ by $2$ .

$a^{8}$