Algebra Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $2 x^{3} y z^{2}$ .

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

Step 2.2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.2.1

Apply the product rule to $2 x^{3} y$ .

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

Step 2.2.2

Apply the product rule to $2 x^{3}$ .

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

Step 2.3

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

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

Step 2.4

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

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Step 2.4.1

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

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

Step 2.4.2

Multiply $3$ by $2$ .

$\frac{1}{4 x^{6} y^{2} {(z^{2})}^{2}}$

Step 2.5

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

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Step 2.5.1

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

$\frac{1}{4 x^{6} y^{2} z^{2 \cdot 2}}$

Step 2.5.2

Multiply $2$ by $2$ .

$\frac{1}{4 x^{6} y^{2} z^{4}}$