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Simplify. Assume all variables are positive. $\newline$ $v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}$ $\newline$ $\newline$ 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. $\newline$ ______ $\newline$

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Simplify expressions involving rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}

\newline

\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

______

\newline

Given expression: We are given the expression $v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}$ and we need to simplify it. According to the laws of exponents, when we multiply two expressions with the same base, we add their exponents.
Multiplying expressions with the same base: Now, we perform the addition of the exponents: $\newline$ $v^{\frac{7}{4}} \cdot v^{\frac{9}{4}} = v^{\frac{7}{4} + \frac{9}{4}}$
Performing addition of exponents: We add the fractions in the exponent: $\frac{7}{4} + \frac{9}{4} = \frac{16}{4}$
Adding fractions in the exponent: We simplify the fraction $\frac{16}{4}$ to its simplest form, which is $4$ : $v^{\frac{16}{4}} = v^4$

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