Algebra Examples

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

Step 1

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

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Step 1.1

Move $x^{- 3}$ .

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

Step 1.2

Multiply $x^{- 3}$ by $x$ .

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Step 1.2.1

Raise $x$ to the power of $1$ .

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

Step 1.2.2

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

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

Step 1.3

Add $- 3$ and $1$ .

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

Step 2

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

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Step 2.1

Move $y^{4}$ .

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

Step 2.2

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

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

Step 2.3

Add $4$ and $4$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Multiply $\frac{3 y^{8}}{x^{2}} \cdot 2$ .

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Step 6.1

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

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

Step 6.2

Multiply $2$ by $3$ .

$\frac{6 y^{8}}{x^{2}}$