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Simplify. Assume all variables are positive. $\newline$ $\frac{b^{\frac{4}{3}}}{b^{\frac{4}{3}} \cdot b^{\frac{1}{3}}}$ $\newline$ 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 radical expressions with variables II

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Q. Simplify. Assume all variables are positive.

\newline

\frac{b^{\frac{4}{3}}}{b^{\frac{4}{3}} \cdot b^{\frac{1}{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

______

Apply Properties of Exponents: Write down the expression and apply the properties of exponents. $\newline$ The expression is $b^{\frac{4}{3}}/(b^{\frac{4}{3}} * b^{\frac{1}{3}})$ . According to the properties of exponents, when you multiply bases that are the same, you add the exponents.
Add Exponents in Denominator: Add the exponents of $b$ in the denominator. $\newline$ The denominator becomes $b^{(4/3 + 1/3)}$ which simplifies to $b^{5/3}$ . $\newline$ So, the expression now is $b^{4/3}/b^{5/3}$ .
Subtract Exponents: Subtract the exponents of $b$ in the numerator and the denominator. $\newline$ According to the properties of exponents, when you divide bases that are the same, you subtract the exponents. $\newline$ $b^{\frac{4}{3}} / b^{\frac{5}{3}} = b^{\frac{4}{3} - \frac{5}{3}} = b^{-\frac{1}{3}}$ .
Write Final Answer: Write the final answer with a positive exponent. $\newline$ Since we assume all variables are positive and we cannot have a negative exponent in the final answer, we write $b^{(-1/3)}$ as $1/b^{(1/3)}$ .

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