Precalculus Examples

$x^{4} {(2 x)}^{5}$

Step 1

Apply the product rule to $2 x$ .

$x^{4} (2^{5} x^{5})$

Step 2

Rewrite using the commutative property of multiplication.

$2^{5} x^{4} x^{5}$

Step 3

Multiply $x^{4}$ by $x^{5}$ by adding the exponents.

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Step 3.1

Move $x^{5}$ .

$2^{5} (x^{5} x^{4})$

Step 3.2

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

$2^{5} x^{5 + 4}$

Step 3.3

Add $5$ and $4$ .

$2^{5} x^{9}$

Step 4

Raise $2$ to the power of $5$ .

$32 x^{9}$