Algebra Examples

$2 x^{3} y^{- 7} \cdot 3 x^{- 2} y^{2}$

Step 1

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

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Step 1.1

Move $x^{- 2}$ .

$2 (x^{- 2} x^{3}) y^{- 7} \cdot (3 y^{2})$

Step 1.2

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

$2 x^{- 2 + 3} y^{- 7} \cdot (3 y^{2})$

Step 1.3

Add $- 2$ and $3$ .

$2 x^{1} y^{- 7} \cdot (3 y^{2})$

Step 2

Simplify $2 x^{1} y^{- 7} \cdot (3 y^{2})$ .

$2 x y^{- 7} \cdot (3 y^{2})$

Step 3

Multiply $y^{- 7}$ by $y^{2}$ by adding the exponents.

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Step 3.1

Move $y^{2}$ .

$2 x (y^{2} y^{- 7}) \cdot 3$

Step 3.2

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

$2 x y^{2 - 7} \cdot 3$

Step 3.3

Subtract $7$ from $2$ .

$2 x y^{- 5} \cdot 3$

Step 4

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

$2 x \frac{1}{y^{5}} \cdot 3$

Step 5

Multiply $2 x \frac{1}{y^{5}}$ .

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Step 5.1

Combine $2$ and $\frac{1}{y^{5}}$ .

$x \frac{2}{y^{5}} \cdot 3$

Step 5.2

Combine $x$ and $\frac{2}{y^{5}}$ .

$\frac{x \cdot 2}{y^{5}} \cdot 3$

Step 6

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

$\frac{2 \cdot x}{y^{5}} \cdot 3$

Step 7

Multiply $\frac{2 x}{y^{5}} \cdot 3$ .

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Step 7.1

Combine $\frac{2 x}{y^{5}}$ and $3$ .

$\frac{2 x \cdot 3}{y^{5}}$

Step 7.2

Multiply $3$ by $2$ .

$\frac{6 x}{y^{5}}$