Question

simplify the expression.
$\frac{y^{\frac{5}{4}} y^{-\frac{1}{4}}}{y^{\frac{1}{3}}}$
write your answer using only positive exponents.
assume that all variables are positive real numbers.

Explanation:

Step1: Add exponents in numerator

When multiplying terms with the same base, add exponents:
$y^{\frac{5}{4}} \cdot y^{-\frac{1}{4}} = y^{\frac{5}{4} + (-\frac{1}{4})} = y^{\frac{5-1}{4}} = y^{\frac{4}{4}} = y^1 = y$

Step2: Divide by denominator term

When dividing terms with the same base, subtract exponents:
$\frac{y}{y^{\frac{1}{3}}} = y^{1 - \frac{1}{3}} = y^{\frac{3}{3} - \frac{1}{3}} = y^{\frac{2}{3}}$

Answer:

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