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Simplify. Assume all variables are positive. $\newline$ $t^{\frac{5}{2}} \cdot t^{\frac{3}{2}}$ $\newline$ 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

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Q. Simplify. Assume all variables are positive.

\newline

t^{\frac{5}{2}} \cdot t^{\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

______

Identify Equation: Identify the equation and apply the product of powers property. $\newline$ The product of powers property states that when you multiply two exponents with the same base, you add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ $t^{\frac{5}{2}} \times t^{\frac{3}{2}} = t^{\left(\frac{5}{2} + \frac{3}{2}\right)}$
Apply Product of Powers: Add the exponents. $\newline$ $(\frac{5}{2}) + (\frac{3}{2}) = \frac{8}{2}$
Add Exponents: Simplify the exponent. $\frac{8}{2} = 4$
Simplify Exponent: Write the final answer with the simplified exponent. $\newline$ $t^{\frac{8}{2}} = t^4$

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1

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(A) The limit exists, and we found it!

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(B) The limit doesn't exist (probably an asymptote).

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(C) The result is indeterminate.

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