Algebra Examples

${(\frac{x^{- 2} y^{- 3}}{2^{0} z^{- 1}})}^{- 2}$

Step 1

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{y^{- 3}}{2^{0} z^{- 1} x^{2}})}^{- 2}$

Step 2

Move $y^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{2^{0} z^{- 1} x^{2} y^{3}})}^{- 2}$

Step 3

Move $z^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

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

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

Step 6

Simplify the numerator.

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Step 6.1

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

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Step 6.1.1

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

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

Step 6.1.2

Multiply $2$ by $2$ .

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

Step 6.2

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

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Step 6.2.1

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

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

Step 6.2.2

Multiply $3$ by $2$ .

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