Algebra Examples

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

Step 1

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

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

Step 2

Multiply $2 y \frac{1}{x}$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Simplify the expression.

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Step 3.1

Move $2$ to the left of $y$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Multiply $2$ by $3$ .

$\frac{2 y}{x} \cdot x^{6}$

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Factor $x$ out of $x^{6}$ .

$\frac{2 y}{x} \cdot (x \cdot x^{5})$

Step 4.2

Cancel the common factor.

$\frac{2 y}{x} \cdot (x \cdot x^{5})$

Step 4.3

Rewrite the expression.

$2 y \cdot x^{5}$

$2 y x^{5}$