Algebra Examples

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

Step 1

Multiply $x^{- 3}$ by $x^{2}$ by adding the exponents.

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Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.2

Add $- 3$ and $2$ .

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

Step 2

Multiply $x^{3}$ by $x^{- 2}$ by adding the exponents.

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Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.2

Subtract $2$ from $3$ .

${(\frac{x^{- 1}}{x^{1}})}^{2}$

Step 3

Simplify $x^{1}$ .

${(\frac{x^{- 1}}{x})}^{2}$

Step 4

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

${(\frac{1}{x \cdot x})}^{2}$

Step 5

Multiply $x$ by $x$ .

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

Step 6

Apply the product rule to $\frac{1}{x^{2}}$ .

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

Step 7

One to any power is one.

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

Step 8

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

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Step 8.1

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

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

Step 8.2

Multiply $2$ by $2$ .

$\frac{1}{x^{4}}$