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Simplify. Assume all variables are positive. $\newline$ $y^{\frac{3}{2}} \times y^{\frac{5}{2}}$ $\newline$ 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. $\newline$ ______

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Simplify expressions involving rational exponents II

Full solution

Q. Simplify. Assume all variables are positive.

\newline

y^{\frac{3}{2}} \times y^{\frac{5}{2}}

\newline

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.

\newline

______

Combine Exponents: Combine the powers of $y$ by adding the exponents. $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $y^{\frac{3}{2}} \times y^{\frac{5}{2}} = y^{\left(\frac{3}{2} + \frac{5}{2}\right)}$
Add Exponents: Perform the addition of the exponents. $(\frac{3}{2}) + (\frac{5}{2}) = \frac{8}{2}$
Simplify Exponent: Simplify the exponent. $\newline$ $\frac{8}{2} = 4$ $\newline$ So, $y^{\frac{3}{2}} \times y^{\frac{5}{2}} = y^4$
Final Answer: Write the final 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. $\newline$ Since $y^4$ is already in the simplest form and the exponent is positive, this is our final answer.

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