Question

Simplify the given expression to rational exponent form, justify each step by identifying the properties of rational exponents used. All work must be shown.

Answer 1

@amistre64

Answer 2

@zkrup
please helpp

Answer 3

@phi

Answer 4

replace the cube root with an exponent 1/3
\[\sqrt[3]{a}= a^\frac{1}{3}\]

Answer 5

in your case, a is \( x^{-6} \)

Answer 6

thank youu @phi

Answer 7

you are not done yet.

Answer 8

i know im trying to figure it out ,

Answer 9

could you show me the steps?

Answer 10

@koribaby :If a number was in the radical with 2 we have :
Power / 2
For example :
\[\sqrt{4}= \sqrt{2^2} = 2^2/2 = 2\]

Answer 11

@koribaby:Got it ?

Answer 12

okayy alittle

Answer 13

One another example :
\[\sqrt{8^4}\]=8^4/2=8^2
Now it s your turn :
\[\sqrt{7^2}\]=?

Answer 14

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Answer 15

\[\frac{ 1 }{ \sqrt[3]{x^{-6}} }= \frac{ 1 }{(x^{-6})^\frac{1}{3}}\]

now use this rule:
\[ \left(a^b\right)^c = a^{bc}\]

in other words, you can change the exponent to -6*1/3 = -2
\[ \frac{ 1 }{x^{-2}} \]

now use one last rule
\[ \frac{1}{a^{-b}} = a^b\]

this rule means
\[ \frac{ 1 }{x^{-2}} = x^2 \]

Answer 16

THX @phi