Algebra Examples

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

Step 1

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

$\frac{1}{{(4 x y^{2})}^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $4 x y^{2}$ .

$\frac{1}{{(4 x)}^{3} {(y^{2})}^{3}}$

Step 2.2

Apply the product rule to $4 x$ .

$\frac{1}{4^{3} x^{3} {(y^{2})}^{3}}$

Step 2.3

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

$\frac{1}{64 x^{3} {(y^{2})}^{3}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{1}{64 x^{3} y^{2 \cdot 3}}$

Step 2.4.2

Multiply $2$ by $3$ .

$\frac{1}{64 x^{3} y^{6}}$