Algebra Examples

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

Step 1

Apply the product rule to $2 a^{3}$ .

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

Step 2

Multiply ${(a^{3})}^{4}$ by ${(a^{3})}^{3}$ by adding the exponents.

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Step 2.1

Move ${(a^{3})}^{3}$ .

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

Step 2.2

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

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

Step 2.3

Add $3$ and $4$ .

$2^{4} {(a^{3})}^{7}$

Step 3

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

$16 {(a^{3})}^{7}$

Step 4

Multiply the exponents in ${(a^{3})}^{7}$ .

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Step 4.1

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

$16 a^{3 \cdot 7}$

Step 4.2

Multiply $3$ by $7$ .

$16 a^{21}$