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

______

Multiply exponents: Multiply $y^{\frac{3}{2}}$ by $y^{\frac{3}{2}}$ . $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $y^{\frac{3}{2}} \times y^{\frac{3}{2}} = y^{\left(\frac{3}{2} + \frac{3}{2}\right)}$
Add exponents: Add the exponents $(\frac{3}{2}) + (\frac{3}{2})$ . $(\frac{3}{2}) + (\frac{3}{2}) = \frac{6}{2}$
Simplify exponent: Simplify the exponent $\frac{6}{2}$ . $\newline$ $\frac{6}{2} = 3$
Write final answer: Write the final answer with the simplified exponent. $y^{\frac{3}{2}} \times y^{\frac{3}{2}} = y^3$

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