Pre-Algebra Examples

$(5 x^{3}) {(2 x)}^{3}$

Step 1

Apply the product rule to $2 x$ .

$5 x^{3} (2^{3} x^{3})$

Step 2

Rewrite using the commutative property of multiplication.

$5 \cdot 2^{3} x^{3} x^{3}$

Step 3

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

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Step 3.1

Move $x^{3}$ .

$5 \cdot 2^{3} (x^{3} x^{3})$

Step 3.2

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

$5 \cdot 2^{3} x^{3 + 3}$

Step 3.3

Add $3$ and $3$ .

$5 \cdot 2^{3} x^{6}$

Step 4

Raise $2$ to the power of $3$ .

$5 \cdot 8 x^{6}$

Step 5

Multiply $5$ by $8$ .

$40 x^{6}$