Algebra Examples

${(x^{3 n} \cdot x^{n - 2})}^{3}$

Step 1

Multiply $x^{3 n}$ by $x^{n - 2}$ by adding the exponents.

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Step 1.1

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

${(x^{3 n + n - 2})}^{3}$

Step 1.2

Add $3 n$ and $n$ .

${(x^{4 n - 2})}^{3}$

Step 2

Multiply the exponents in ${(x^{4 n - 2})}^{3}$ .

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Step 2.1

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

$x^{(4 n - 2) \cdot 3}$

Step 2.2

Apply the distributive property.

$x^{4 n \cdot 3 - 2 \cdot 3}$

Step 2.3

Multiply $3$ by $4$ .

$x^{12 n - 2 \cdot 3}$

Step 2.4

Multiply $- 2$ by $3$ .

$x^{12 n - 6}$