Question

Find the rational exponent.

• Simplify each expression using the rules of exponents and examine the steps you are taking.

Answer 1

\[\frac{ a ^{\frac{ 1 }{ 2 }} }{ a ^{2} }\]

Answer 2

\[\frac{ 1 }{ a ^{-\frac{ 1 }{ 2 }} }\]

Answer 3

\[\frac{ 1 }{ a ^{2} a ^{-\frac{ 1 }{ 2 }}}\]

Answer 4

\[\frac{ 1 }{ a ^{2-\frac{ 1 }{ 2 }} } = \frac{ 1 }{ a ^{\frac{ 3 }{ 2 }} } = 1/\sqrt{a ^{3}}\]

Answer 5

"Simplify" is a funny thing. It's particularly funny how "simplify" can mean to make a total mess and call it better. I would recommend \(a^{-3/2}\) on this one.

Answer 6

Rule of exponent you need on this one is:
\(\huge \frac{a^m}{a^n}=a^{m-n}\)

Answer 7

@mathmate which one is the simplest form

Answer 8

a ^-3/2

Answer 9

?

Answer 10

Please help me out. i need to find out the simplest form

Answer 11

@rock_mit182
Yes, your answer is correct, here's why:
\(\huge \frac{a^{1/2}}{a^2}=a^{1/2-2}=a^{-3/2}\)

Answer 12

i don't have to rationalize ?

Answer 13

Yes, you do have to rationalize, but only when you need to.
You do not have a radical in the denominator, just a negative fractional exponent, so no need.

Answer 14

ok thanks

Answer 15

You're welcome! :)

Answer 16

\[(\frac{ a ^{\frac{ 1 }{ 4 }} }{ a })^{2}\]

Answer 17

\[\frac{ (a ^{\frac{ 1 }{ 4 }})^{2} }{ (a)^{2} }\]

Answer 18

Use the law of exponents:
\(\large (a^m)^n=a^{mn}\)

Answer 19

There is no such thing as a "simplest form". It's subjective.