Finite Math Examples

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

Step 1

Move $x^{\frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 2

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

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

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

Move $x^{- \frac{2}{3}}$ .

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

Step 3.1.2

Multiply $x^{- \frac{2}{3}}$ by $x$ .

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Step 3.1.2.1

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

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

Step 3.1.2.2

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

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

Step 3.1.3

Write $1$ as a fraction with a common denominator.

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

Step 3.1.4

Combine the numerators over the common denominator.

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

Step 3.1.5

Add $- 2$ and $3$ .

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

Step 3.2

Multiply $y^{2}$ by $y^{- \frac{1}{2}}$ by adding the exponents.

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Step 3.2.1

Move $y^{- \frac{1}{2}}$ .

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

Step 3.2.2

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

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

Step 3.2.3

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.2.4

Combine $2$ and $\frac{2}{2}$ .

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

Step 3.2.5

Combine the numerators over the common denominator.

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

Step 3.2.6

Simplify the numerator.

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Step 3.2.6.1

Multiply $2$ by $2$ .

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

Step 3.2.6.2

Add $- 1$ and $4$ .

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