Precalculus Examples

${(2 a^{3} a^{5})}^{4}$

Step 1

Multiply $a^{3}$ by $a^{5}$ by adding the exponents.

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Step 1.1

Move $a^{5}$ .

${(2 (a^{5} a^{3}))}^{4}$

Step 1.2

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

${(2 a^{5 + 3})}^{4}$

Step 1.3

Add $5$ and $3$ .

${(2 a^{8})}^{4}$

Step 2

Apply the product rule to $2 a^{8}$ .

$2^{4} {(a^{8})}^{4}$

Step 3

Raise $2$ to the power of $4$ .

$16 {(a^{8})}^{4}$

Step 4

Multiply the exponents in ${(a^{8})}^{4}$ .

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Step 4.1

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

$16 a^{8 \cdot 4}$

Step 4.2

Multiply $8$ by $4$ .

$16 a^{32}$