Square root simplification?

Question

How does this work out?

where x^(1/3) times 3x^2
(the third root of x) times (three x squared)

becomes
x times 9x^2
(x) times (9 x squared)

How does that work out?? It seems to me that it should come out to be:

3 x^(7/3)
(3 x to the seven/thirds power)

Answer 1

Forget the coefficient of 3 for the moment. Recall that

(x^a)(x^b) = x^(a+b)

So x^(1/3) * x^2 = x^(1/3 + 2) = x^(7/3)

The coefficient just sits out front. Thus,

x^(1/3) * 3x^2 = 3x^(7/3)

Answer 2

if you mean cube root of X times 3 square root of X. the answer would be:

X raised to the 1/3 power times 3 X raise to 1/2 power.
1/3 power times 1/2 power = 1/6 power
3 X to the 1/6 power is the answer.

Answer 3

Rule is (x^a)(x^b) = x^(a + b)

3 (x ²) x^(1/3) = 3 x ^ (7/3)

Answer 4

third root of x cubed j3X