Question

Rewrite in simplest radical form
1
x
−3
6
. Show each step of your process.

Answer 1

@ospreytriple

Answer 2

First, I would reduce the exponent of x. What do you get?

Answer 3

-1/2

Answer 4

Right on. So now you have\[\frac{ 1 }{ x ^{-\frac{ 1 }{ 2 }} }\]Is that right?

Answer 5

yes

Answer 6

OK, I hope you will agree that\[\frac{ 1 }{ x ^{-\frac{ 1 }{ 2 }} } = \left( \frac{ 1 }{ x } \right)^{-\frac{ 1 }{ 2 }}\]You OK with that?

Answer 7

yes

Answer 8

Perfect. Now, to invert the base, you must change the sign of the exponent. For example,\[3^{-2} = \left( \frac{ 1 }{ 3 } \right)^{2}\] or\[\left( \frac{ 1 }{ 4 } \right)^{5} = 4^{-5}\]Gwt the idea? You need to do the same thing with\[\left( \frac{ 1 }{ x } \right)^{-\frac{ 1 }{ 2 }}\]What do you get?

Answer 9

x to the pwer of 2?

Answer 10

Don't invert the exponent, just change its sign. Invert the BASE, and change the sign on the EXPONENT. Try again?

Answer 11

x to the power of 1/2?

Answer 12

Perfect. Now write it in radical form.

Answer 13

In general, fractional exponents are written in radical form like this:\[x ^{\frac{ a }{ b }} = \sqrt[b]{x ^{a}}\]

Answer 14

\[\sqrt{x}\]

Answer 15

Well done!

Answer 16

thank you again!