Question

I have a question on alg 2

Answer 1

IM in algebra two...ill try to help but i apologize if i cant

Answer 2

\[\frac{ 1 }{ \sqrt[3]{6^{-6}} }\]

Answer 3

It wants me to simplify in radical form and justify each step by identifying the properties of rational exponents used

Answer 4

do u have any choices?

Answer 5

I would change \[ \sqrt[3]{stuff} = stuff^\frac{1}{3} \]

Answer 6

just a minute. ive never seen this before but i think i might be able to try to solve it?

Answer 7

unless there are some answers idk. im sorry. the answer i got is probably wayyyyyy offf i think i got

if thats not right im sorry. i have to go now. bye

Answer 8

Alright thanks haha

Answer 9

one way to do this is first convert from "radical" form to "exponent" form
using the rule
\[ \sqrt[a]{b}= b^\frac{1}{a} \]
You would re-write
\[ \frac{ 1 }{ \sqrt[3]{6^{-6}} } = \frac{ 1 }{\left(6^{-6}\right)^\frac{1}{3}} \]

if we concentrate just on the bottom, we can use this rule
\[ \left(a^b \right)^c = a^{b\cdot c} \]
to write
\[ \left(6^{-6}\right)^\frac{1}{3} = 6^{-6\cdot \frac{1}{3}}= 6^{-2}\]
and you now have
\[ \frac{ 1 }{6^{-2} }\]

there is another rule: you can "flip" the fraction using this:
\[ a^{-b} = \frac{1}{ a^{b}} \] or
\[ a^b= \frac{1}{ a^{-b}} \]

in other words,
\[ \frac{ 1 }{6^{-2} } = 6^2\]
Finally
\[ 6^2 = 36\]