Algebra Examples

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

Step 1

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

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Step 1.1

Move $x^{- 2}$ .

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

Step 1.2

Multiply $x^{- 2}$ by $x$ .

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Step 1.2.1

Raise $x$ to the power of $1$ .

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

Step 1.2.2

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

$2 x^{- 2 + 1} \cdot \frac{1}{x^{- 3}}$

Step 1.3

Add $- 2$ and $1$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Combine $2$ and $\frac{1}{x}$ .

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

Step 5

Combine.

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

Step 6

Multiply $2$ by $1$ .

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

Step 7

Combine $x$ and $\frac{1}{x^{3}}$ .

$\frac{2}{\frac{x}{x^{3}}}$

Step 8

Reduce the expression $\frac{x}{x^{3}}$ by cancelling the common factors.

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Step 8.1

Raise $x$ to the power of $1$ .

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

Step 8.2

Factor $x$ out of $x^{1}$ .

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

Step 8.3

Factor $x$ out of $x^{3}$ .

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

Step 8.4

Cancel the common factor.

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

Step 8.5

Rewrite the expression.

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

Step 9

Multiply the numerator by the reciprocal of the denominator.

$2 x^{2}$