Simplify (x^(2/3)y^(5/6))/(x^(-1/3)y^(1/2))

$\frac{x^{\frac{2}{3}} y^{\frac{5}{6}}}{x^{- \frac{1}{3}} y^{\frac{1}{2}}}$

Step 1

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

$\frac{x^{\frac{2}{3}} y^{\frac{5}{6}} x^{\frac{1}{3}}}{y^{\frac{1}{2}}}$

Step 2

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

$x^{\frac{2}{3}} y^{\frac{5}{6}} x^{\frac{1}{3}} y^{- \frac{1}{2}}$

Step 3

Multiply $x^{\frac{2}{3}}$ by $x^{\frac{1}{3}}$ by adding the exponents.

Move $x^{\frac{1}{3}}$ .

$x^{\frac{1}{3}} x^{\frac{2}{3}} y^{\frac{5}{6}} y^{- \frac{1}{2}}$

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

$x^{\frac{1}{3} + \frac{2}{3}} y^{\frac{5}{6}} y^{- \frac{1}{2}}$

Combine the numerators over the common denominator.

$x^{\frac{1 + 2}{3}} y^{\frac{5}{6}} y^{- \frac{1}{2}}$

Add $1$ and $2$ .

$x^{\frac{3}{3}} y^{\frac{5}{6}} y^{- \frac{1}{2}}$

Divide $3$ by $3$ .

$x^{1} y^{\frac{5}{6}} y^{- \frac{1}{2}}$

Step 4

Simplify $x^{1} y^{\frac{5}{6}}$ .

$x y^{\frac{5}{6}} y^{- \frac{1}{2}}$

Step 5

Multiply $y^{\frac{5}{6}}$ by $y^{- \frac{1}{2}}$ by adding the exponents.

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

$x (y^{- \frac{1}{2}} y^{\frac{5}{6}})$

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

$x y^{- \frac{1}{2} + \frac{5}{6}}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x y^{- \frac{1}{2} \cdot \frac{3}{3} + \frac{5}{6}}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$x y^{- \frac{3}{2 \cdot 3} + \frac{5}{6}}$

Multiply $2$ by $3$ .

$x y^{- \frac{3}{6} + \frac{5}{6}}$

Combine the numerators over the common denominator.

$x y^{\frac{- 3 + 5}{6}}$

Add $- 3$ and $5$ .

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

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

$x y^{\frac{2 (1)}{6}}$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (x^(2/3)y^(5/6))/(x^(-1/3)y^(1/2))

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