Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Multiply $2$ by $- 2$ .

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

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(3 x^{3})}^{4}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $3 x^{3}$ .

$\frac{1}{3^{4} {(x^{3})}^{4}}$

Step 3.2

Raise $3$ to the power of $4$ .

$\frac{1}{81 {(x^{3})}^{4}}$

Step 3.3

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

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Step 3.3.1

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

$\frac{1}{81 x^{3 \cdot 4}}$

Step 3.3.2

Multiply $3$ by $4$ .

$\frac{1}{81 x^{12}}$