Pre-Algebra Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $5 x^{3}$ .

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

Step 2.2

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

$\frac{1}{25 {(x^{3})}^{2}}$

Step 2.3

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

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Step 2.3.1

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

$\frac{1}{25 x^{3 \cdot 2}}$

Step 2.3.2

Multiply $3$ by $2$ .

$\frac{1}{25 x^{6}}$