Question

Help, Please? Thank you:))

Answer 1

Could I please have some help on solving this \[\frac{ 1 }{ \sqrt[3]{x ^{-6}} }\]

Answer 2

rewrite the denominator as \[\large \sqrt[n]{x^m} \implies x^{m/n}\]

Answer 3

So: \(\large \sqrt[3]{x^{-6}} = x^{-6/3} = x^?\)

Answer 4

\[x ^{2}\]

Answer 5

Forgetting a sign.

Answer 6

Correct? Would that be all to do?

Answer 7

Oh the (-)!!

Answer 8

\[x^{-2}\]

Answer 9

\[\large x^{-6/3}=x^{-2}\]\[\frac{1}{x^{-\#}} \iff x^{+\#}\]

Answer 10

Therefore \[\frac{1}{x^{-2}} = x^{2}\]

Answer 11

Did it turn into a positive because the 1 is positive, or is that just a rule?

Answer 12

It's just the rule.

Answer 13

Is there a name to it, would you happen to know?

Answer 14

If you have a negative in the denominator, raise it to the numerator, vice versa.

Answer 15

Oh okay, thank you very much!!

Answer 16

Just remember: \[x^{-\#} = \frac{1}{x^{\#}}~,~ \frac{1}{x^{-\#}} = x^{\#}\]

Answer 17

Thank you:)!!

Answer 18

No problem.