Question

simplify the expression.

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

write your answer using only positive exponents. assume that all variables are positive real numbers.

Explanation:

Identify the given expression

The given expression to simplify is:

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

Simplify the denominator

Using the Exponent Rules knowledge point

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

Simplify the quotient

Using the Exponent Rules and Fraction Subtraction knowledge points

$$ \frac{y^{\frac{1}{3}}}{y^{-1}} = y^{\frac{1}{3} - (-1)} = y^{\frac{1}{3} + 1} = y^{\frac{4}{3}} $$

Answer:

\(y^{\frac{4}{3}}\)