Simplify yx^(1/3)*xy^(3/2)

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

Step 1

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

Move $y^{\frac{3}{2}}$ .

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

Multiply $y^{\frac{3}{2}}$ by $y$ .

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $3$ and $2$ .

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

Step 2

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

Move $x$ .

$y^{\frac{5}{2}} (x \cdot x^{\frac{1}{3}})$

Multiply $x$ by $x^{\frac{1}{3}}$ .

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $3$ and $1$ .

$y^{\frac{5}{2}} x^{\frac{4}{3}}$