Question

URGENT: I need help ASAP
(4^1/2•2^1/3)^-8

Can someone please help I'm so lost thank you :)

Answer 1

does it help to know that \(4^{\frac{1}{2}}=\sqrt4=2\)?

Answer 2

Yes well I'm a bit confused. Do I solve the problem in parenthesis first then multiply the exponent on the outside?

Answer 3

we got \[(2\times 2^{\frac{1}{3}})^{-8}\] right ?

Answer 4

But then again, the inside would give me 2• 2• 3 cube root 2 which confuses me now.

Answer 5

I understand that so far yes

Answer 6

add the exponents inside get \[\left(2^{\frac{4}{3}}\right)^{-8}\]

Answer 7

on account of \(1+\frac{1}{3}=\frac{4}{3}\)

Answer 8

Wait how did you get 4?

Answer 9

then multiply the exponents

Answer 10

How would you add the exponents 1+1/3 and get 4/3?

Answer 11

\[\huge 2\times 2^{\frac{1}{3}}=2^1\times 2^{\frac{1}{3}}=2^{1+\frac{1}{3}}\]

Answer 12

and \[1+\frac{1}{3}=\frac{4}{3}\]

Answer 13

are you asking why \(1+\frac{1}{3}=\frac{4}{3}\)?

Answer 14

cause i can explain that if you like

Answer 15

But wouldn't it be 1 1/3 ?

Answer 16

yes same number

Answer 17

Yes I don't understand how you got 4/3 when adding 1+ 1/3

Answer 18

do you know how to turn a mixed number in to an "improper fraction"?

Answer 19

\[\huge 1\tfrac{1}{3}=\frac{3\times 1+1}{3}=\frac{4}{3}\]

Answer 20

Oh wait it's the same thing when divided into decimal format okay I understand

Answer 21

I understand that part okay

Answer 22

nothing to do with decimals, just adding a fraction and a whole number

Answer 23

finally multiply \(\frac{4}{3}\times (-8)\)

Answer 24

Then 4/3 multiply it by -8 to get -4/3 so it would be 4^-4/3 correct?

Answer 25

\[\frac{4}{3}\times (-8)\neq -\frac{4}{3}\]

Answer 26

\[4\times 8=32\] so
\[\frac{4}{3}\times (-8)=-\frac{32}{3}\]

Answer 27

That's a large number. Okay I understand that

Answer 28

it is not large
first off it is negative
second it is \(-10\tfrac{2}{3}\)

Answer 29

in any case your answer is \[\huge 2^{-\frac{32}{3}}\]

Answer 30

Oh.

Answer 31

So the correct answer would be -10^2/3 or 2^-32/3 or are they both considered the same?

Answer 32

answer would not be \[-10^{\frac{ 2 }{ 3 }}\]
satellite was merely explaining that \[-\frac{ 32 }{ 3 }=-10\frac{ 2 }{ 3 }\]

The correct answer would be \[2^-{\frac{ 32 }{ 2 }} or \frac{ 1 }{( \sqrt{2}^{32}) }\]

Answer 33

Thank you very much I understand now :)