Simplify. Assume all variables are positive. $\newline$ $b^{\frac{11}{5}} \cdot b^{\frac{12}{5}}$ $\newline$ 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. $\newline$ ______

Full solution

Q. Simplify. Assume all variables are positive.

\newline

b^{\frac{11}{5}} \cdot b^{\frac{12}{5}}

\newline

Write your answer in the form

A

\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 Exponent Rule: Identify the equation and apply the exponent multiplication rule. $\newline$ When multiplying two exponents with the same base, we add the exponents: $\newline$ $b^{\frac{m}{n}} \times b^{\frac{p}{q}} = b^{\left(\frac{m}{n} + \frac{p}{q}\right)}$ $\newline$ So, $b^{\frac{11}{5}} \times b^{\frac{12}{5}} = b^{\left(\frac{11}{5} + \frac{12}{5}\right)}$
Add Exponents: Add the exponents. $\newline$ $(\frac{11}{5}) + (\frac{12}{5}) = (\frac{11 + 12}{5})$ $\newline$ $= \frac{23}{5}$ $\newline$ So, $b^{(\frac{11}{5})} \cdot b^{(\frac{12}{5})} = b^{(\frac{23}{5})}$
Write Final Answer: 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 $b^{\frac{23}{5}}$ , which is already in the correct form.