what is the answer to 8 to the 2/3 power times 4 to the 3/2 power???

8^(2/3) x 4^(3/2)
4 x 8
32

[8^(2/3)][4^(3/2)] =
[2²][2³] =
4(8) =
32

i think of what the question is getting at is how might you simplify the formulation. In maths in basic terms equations might nicely be solved, and (a^2 * a^4) ^2 isn't an equation, equations have an equals sign in the midst of them, case in point a^2 + a million = 17 is an equation. so as to simplify the formulation in the question you will possibly say: a^2 is the comparable as a*a a^4 is the comparable as a*a*a*a subsequently (a^2 * a^4) is the comparable as a*a*a*a*a*a and (a^2 * a^4)^2 is the comparable as (a^2 * a^4) * (a^2 * a^4) which in turn is the comparable as (a*a*a*a*a*a) * (a*a*a*a*a*a) that's the comparable as a*a*a*a*a*a*a*a*a*a*a*a that's basically a^12 so a simplified form of (a^2 * a^4)^2 is a^12

a^(m/n) = n√a^m

8^(2/3) x 4^(3/2)
= 3√8^2 x √4^3
= 3√64 x √64
= 4 x 8
= 32

3√ = extract the cube root

First simplify (4^3/2).

= [2^(2*1/2*3)] = [2^3] = 8.

Then simplify 8^2/3.

= [2^(3*1/3*2)] = [2^2] = 4.

Then multiply 4*8 = 32. :-)

(8)^2/3 × (4)^3/2
= cube root 8^2 × square root 4^3
= cube root 64 × square root 64
= 4 × 8 = 32

4*8 = 32

Well to analyze the problem, there are two answers:

8^2/3 is the same as four, because 8 cubed is two, then square it and you get four.

4^3/2 is the same as the same as eight; do the same process (root by the denominator, and put the answer to the power of the numerator); soooo...we have four square rooted, which is 2, then we take two and cube it to equal eight.

Now you have four multiplied by eight= 32