Algebra Examples

$\frac{4 x^{3}}{y^{2}} \cdot \frac{y^{- 3} x^{- 2}}{8 x^{- 1}}$

Step 1

Combine.

$\frac{4 x^{3} (y^{- 3} x^{- 2})}{y^{2} (8 x^{- 1})}$

Step 2

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

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Step 2.1

Move $x^{- 2}$ .

$\frac{4 (x^{- 2} x^{3}) y^{- 3}}{y^{2} (8 x^{- 1})}$

Step 2.2

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

$\frac{4 x^{- 2 + 3} y^{- 3}}{y^{2} (8 x^{- 1})}$

Step 2.3

Add $- 2$ and $3$ .

$\frac{4 x^{1} y^{- 3}}{y^{2} (8 x^{- 1})}$

Step 3

Simplify $4 x^{1} y^{- 3}$ .

$\frac{4 x y^{- 3}}{y^{2} (8 x^{- 1})}$

Step 4

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

$\frac{4 x}{y^{2} (8 x^{- 1}) y^{3}}$

Step 5

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

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Step 5.1

Move $y^{3}$ .

$\frac{4 x}{y^{3} y^{2} (8 x^{- 1})}$

Step 5.2

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

$\frac{4 x}{y^{3 + 2} (8 x^{- 1})}$

Step 5.3

Add $3$ and $2$ .

$\frac{4 x}{y^{5} (8 x^{- 1})}$

Step 6

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

$\frac{4 x \cdot x}{y^{5} \cdot 8}$

Step 7

Multiply $x$ by $x$ by adding the exponents.

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Step 7.1

Move $x$ .

$\frac{4 (x \cdot x)}{y^{5} \cdot 8}$

Step 7.2

Multiply $x$ by $x$ .

$\frac{4 x^{2}}{y^{5} \cdot 8}$

Step 8

Cancel the common factor of $4$ and $8$ .

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Step 8.1

Factor $4$ out of $4 x^{2}$ .

$\frac{4 (x^{2})}{y^{5} \cdot 8}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $4$ out of $y^{5} \cdot 8$ .

$\frac{4 (x^{2})}{4 (y^{5} \cdot 2)}$

Step 8.2.2

Cancel the common factor.

$\frac{4 x^{2}}{4 (y^{5} \cdot 2)}$

Step 8.2.3

Rewrite the expression.

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

Step 9

Move $2$ to the left of $y^{5}$ .

$\frac{x^{2}}{2 y^{5}}$