How would I work out (8^1/2)^2/3 * 4^-3?

Question

Without a calculator step by step please. So that means the 2/3 and 1/2 are 2over3 and 1over2 as the division in the head is impossible.

Thanks.

Answer 1

(8^1/2)^2/3=8^1/3=2
4^-3=1/4^3=1/64
so(8^1/2)^2/3*4^-3=2/64=1/32

Answer 2

( 8 ^ 1/2) ^ 2/3 * 4 ^ -3

(8 ) ^ (1/2)*(2/3)*(1/4^3)
(8) ^ (1/3) * (1 / 64)
(2) ^ (1 / 64)

to use your calculator :
press 1 / 64 and save your result
press 2 then X^y your saving , You will get the result
If you inverse it you will get 32
as the correct answer is 1/32

Answer 3

8^1/2 is root 8.

Then, root 8 taken to the 2/3 power is the cube root of root 8, squared, which is just the cube root of 8, which is just 2.

So the left hand side is 2. Multiply that by 1 over 4^3, which is 1 over 64.

You are left with the final answer, 1/32.

Answer 4

(8^1/2) ^ 2/3 * (4^-3) = (8^1/3) * (1/4^3) = 2 * (1/2^6) = 1/2^ 5 = 1/32 ...

understood the algebraic rules of exponents involved here?

Answer 5

= 8^[(1/2)*(2/3)] * 4^-3 =8^(1/3) * 4^-3= 8^(1/3) * 1/[4^3] = 2*(1/64)=1/32 = 0.03125

Answer 6

okay this means the Square root of Square root of 8 all cubed times 1 over 4 cubed. Just look at it that way

Answer 7

well a little hint
16= 2^4=2*2*2*2
and
2=16^1/4

Answer 8

(8^(1/2))^(2/3) * (4^(-3))

8^((1/2) * (2/3)) * (1/(4^3))

8^(2/6) * (1/64)

8^(1/3) * (1/64)

2 * (1/64)

2/64

ANS : (1/32)

Answer 9

(8^1/2)^2/3=8^1/3=2
4^-3=1/4^3=1/64
so(8^1/2)^2/3*4^-3=2/64=1/32

Answer 10

that is 8^(1/2*2/3)*4(-3)
=8^(1/3)*4(-3)=(2^3)^1/3*4^(-3)=2^(3*1/3)*2^(-6)=2*2^(-6)=2^(-5)
But one thing I don`t get:
it`s (1/2)^2/3
Or (8^1/2)^2/3
Good luck