Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

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

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Step 3.1

Move $x^{2}$ .

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

Step 3.2

Multiply $x^{2}$ by $x$ .

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $2$ and $1$ .

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

Step 4

Move $y^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{2 y^{3} y^{4}}{3 x^{3}}$

Step 5

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

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Step 5.1

Move $y^{4}$ .

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

Step 5.2

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

$\frac{2 y^{4 + 3}}{3 x^{3}}$

Step 5.3

Add $4$ and $3$ .

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