Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

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Step 2.1

Move $x^{5}$ .

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

Step 2.2

Multiply $x^{5}$ by $x$ .

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Step 2.2.1

Raise $x$ to the power of $1$ .

${(2 \cdot 3 (x^{5} x^{1}))}^{3}$

Step 2.2.2

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

${(2 \cdot 3 x^{5 + 1})}^{3}$

Step 2.3

Add $5$ and $1$ .

${(2 \cdot 3 x^{6})}^{3}$

Step 3

Multiply $2$ by $3$ .

${(6 x^{6})}^{3}$

Step 4

Apply the product rule to $6 x^{6}$ .

$6^{3} {(x^{6})}^{3}$

Step 5

Raise $6$ to the power of $3$ .

$216 {(x^{6})}^{3}$

Step 6

Multiply the exponents in ${(x^{6})}^{3}$ .

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Step 6.1

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

$216 x^{6 \cdot 3}$

Step 6.2

Multiply $6$ by $3$ .

$216 x^{18}$