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

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{b^{\frac{3}{2}}}{b^{\frac{1}{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 the Expression: We have the expression: $\newline$ $b^{\frac{3}{2}} / b^{\frac{1}{2}}$ $\newline$ Which operation will be applied with the exponents? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Apply Exponent Rule: Apply the exponent rule for division: $b^{\frac{3}{2}} / b^{\frac{1}{2}} = b^{\frac{3}{2} - \frac{1}{2}} = b^{\frac{2}{2}} = b^1$
Simplify the Expression: Simplify the expression: $\newline$ Since $b^1$ is simply $b$ , the final simplified form is: $\newline$ $b$

More problems from Simplify expressions involving rational exponents

Question

h(x)=\log _{2}(x)

\newline

Can we use the mean value theorem to say the equation

h^{\prime}(x)=1

has a solution where

1<x<2

\newline

1

\newline

(A) No, since the function is not differentiable on that interval.

\newline

(B) No, since the average rate of change of

h

over the interval

1 \leq x \leq 2

1

\newline

(C) Yes, both conditions for using the mean value theorem have been met.

Posted 9 months ago

Question

What is the sign of

39 \frac{11}{13}+\left(-41 \frac{1}{13}\right) \text { ? }

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 9 months ago

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What is the sign of

-1042+1042 ?

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

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What is the sign of

-18 \frac{9}{17}+\left(-18 \frac{9}{17}\right)

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 9 months ago

Question

What is the sign of

\frac{23}{45}+\left(-\frac{23}{45}\right) ?

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 9 months ago

Question

What is the sign of

45+(-38)

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 9 months ago

Question

What is the sign of

-49.8+61.2

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 9 months ago

Question

What is the sign of

-1.69+(-1.69) ?

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 9 months ago

Question

What is the sign of

37+(-37)

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 9 months ago

Question

\begin{array}{l} g(x)=\sqrt{2 x-9} \\ g^{\prime}(x)=? \end{array}

\newline

1

\newline

\frac{\sqrt{2 x-9}}{2}

\newline

\frac{1}{\sqrt{2 x-9}}

\newline

\frac{1}{2 \sqrt{2 x-9}}

\newline

\frac{1}{\sqrt{x}}

Posted 9 months ago

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