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Simplify. Assume all variables are positive. $\newline$ $y^{\frac{8}{3}} \cdot y^{\frac{7}{3}}$ $\newline$ 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

y^{\frac{8}{3}} \cdot y^{\frac{7}{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 and Apply Property: Identify the equation and apply the property of exponents for multiplication. $\newline$ When multiplying two exponents with the same base, we add the exponents: $\newline$ $a^m \times a^n = a^{(m+n)}$ $\newline$ So, $y^{\frac{8}{3}} \times y^{\frac{7}{3}}$ becomes $y^{\frac{8}{3} + \frac{7}{3}}$ .
Add Exponents: Add the exponents. $\newline$ $\frac{8}{3} + \frac{7}{3} = \frac{15}{3}$
Simplify Fraction: Simplify the fraction $\frac{15}{3}$ . $\newline$ $\frac{15}{3} = 5$
Write Final Expression: Write the final expression using the simplified exponent. $y^{(15/3)}$ simplifies to $y^5$ .

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