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Simplify. Assume all variables are positive. $\newline$ $b^{\frac{1}{2}} \cdot b^{\frac{3}{2}}$ $\newline$ 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

b^{\frac{1}{2}} \cdot b^{\frac{3}{2}}

\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 product of powers property. $\newline$ The product of powers property states that when multiplying like bases, you add the exponents: $a^m \times a^n = a^{(m+n)}$ . $\newline$ $b^{(1/2)} \times b^{(3/2)} = b^{(1/2 + 3/2)}$
Add Exponents: Add the exponents. $\newline$ $\frac{1}{2} + \frac{3}{2} = \frac{4}{2}$
Simplify Fraction: Simplify the fraction $\frac{4}{2}$ . $\frac{4}{2} = 2$
Write Final Answer: Write the final answer using the simplified exponent. $b^{\frac{4}{2}} = b^2$

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f(x)=\frac{6 x+5}{2-\sqrt{14+5 x}}

\newline

We want to find

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What happens when we use direct substitution?

\newline

1

\newline

(A) The limit exists, and we found it!

\newline

(B) The limit doesn't exist (probably an asymptote).

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(C) The result is indeterminate.

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