Pre-Algebra Examples

$(2 x^{- 3} y^{- 4}) (6 x^{- 4} y^{7})$

Step 1

Multiply $x^{- 3}$ by $x^{- 4}$ by adding the exponents.

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Step 1.1

Move $x^{- 4}$ .

$2 (x^{- 4} x^{- 3}) y^{- 4} (6 y^{7})$

Step 1.2

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

$2 x^{- 4 - 3} y^{- 4} (6 y^{7})$

Step 1.3

Subtract $3$ from $- 4$ .

$2 x^{- 7} y^{- 4} (6 y^{7})$

Step 2

Multiply $y^{- 4}$ by $y^{7}$ by adding the exponents.

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Step 2.1

Move $y^{7}$ .

$2 x^{- 7} (y^{7} y^{- 4}) \cdot 6$

Step 2.2

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

$2 x^{- 7} y^{7 - 4} \cdot 6$

Step 2.3

Subtract $4$ from $7$ .

$2 x^{- 7} y^{3} \cdot 6$

Step 3

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

$2 \frac{1}{x^{7}} y^{3} \cdot 6$

Step 4

Combine $2$ and $\frac{1}{x^{7}}$ .

$\frac{2}{x^{7}} y^{3} \cdot 6$

Step 5

Combine $\frac{2}{x^{7}}$ and $y^{3}$ .

$\frac{2 y^{3}}{x^{7}} \cdot 6$

Step 6

Multiply $\frac{2 y^{3}}{x^{7}} \cdot 6$ .

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Step 6.1

Combine $\frac{2 y^{3}}{x^{7}}$ and $6$ .

$\frac{2 y^{3} \cdot 6}{x^{7}}$

Step 6.2

Multiply $6$ by $2$ .

$\frac{12 y^{3}}{x^{7}}$