Question

simplify. assume all variables are positive.$y^{\frac{13}{5}} cdot y^{\frac{2}{5}}$write your answer in the form a or $\frac{a}{b}$, where a and b are constants or variable expressions that have no variables in common. all exponents in your answer should be positive.

Explanation:

Step1: Apply exponent product rule

When multiplying like bases, add exponents: $y^a \cdot y^b = y^{a+b}$
So, $y^{\frac{13}{5}} \cdot y^{\frac{2}{5}} = y^{\frac{13}{5}+\frac{2}{5}}$

Step2: Add the exponents

$\frac{13}{5}+\frac{2}{5} = \frac{15}{5} = 3$
Thus, $y^{\frac{15}{5}} = y^3$

Answer:

$y^3$