Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

$2 x^{- 1} y^{4} (x^{- 2} y^{4})$

Step 2

Multiply $x^{- 1}$ by $x^{- 2}$ by adding the exponents.

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Step 2.1

Move $x^{- 2}$ .

$2 (x^{- 2} x^{- 1}) y^{4} y^{4}$

Step 2.2

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

$2 x^{- 2 - 1} y^{4} y^{4}$

Step 2.3

Subtract $1$ from $- 2$ .

$2 x^{- 3} y^{4} y^{4}$

Step 3

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

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Step 3.1

Move $y^{4}$ .

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

Step 3.2

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

$2 x^{- 3} y^{4 + 4}$

Step 3.3

Add $4$ and $4$ .

$2 x^{- 3} y^{8}$

Step 4

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

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

Step 5

Combine $2$ and $\frac{1}{x^{3}}$ .

$\frac{2}{x^{3}} y^{8}$

Step 6

Combine $\frac{2}{x^{3}}$ and $y^{8}$ .

$\frac{2 y^{8}}{x^{3}}$