Calculus Examples

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

Step 1

Apply the product rule to $2 b$ .

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

Step 2

Rewrite using the commutative property of multiplication.

$2^{4} b^{8} b^{4}$

Step 3

Multiply $b^{8}$ by $b^{4}$ by adding the exponents.

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Step 3.1

Move $b^{4}$ .

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

Step 3.2

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

$2^{4} b^{4 + 8}$

Step 3.3

Add $4$ and $8$ .

$2^{4} b^{12}$

Step 4

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

$16 b^{12}$