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

\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: $a^m \times a^n = a^{m+n}$ . $\newline$ $t^{\frac{5}{3}} \times t^{\frac{5}{3}} = t^{\frac{5}{3} + \frac{5}{3}}$
Apply Product of Powers: Add the exponents. $\newline$ $\frac{5}{3} + \frac{5}{3} = \frac{10}{3}$ $\newline$ So, $t^{\frac{5}{3}} \times t^{\frac{5}{3}} = t^{\frac{10}{3}}$
Add Exponents: 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. $\newline$ The final answer is $t^{\frac{10}{3}}$ , which is already in the correct form.

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