# Question: Simplification with Cube Roots

## Comment on Simplification with Cube Roots

### Can this also be done the

Can this also be done the following way:

- Cross off one of the four 3 sq root of 6 (numerator) and the eight 3 sq root of 6 (denominator) to equal 2. Divide the 4 on the numerator by 2 on the denominator to equal E, two 3 sq root of 6

### Is it safe to say:

Is it safe to say:
(Cube root 6)^2/(Cube root 6) = Cube root 6
something like x^2/x = x

### Yes, we can say that

Yes, we can say that

Think of it this way:
(cube root 6)²/(cube root 6) = (cube root 6)(cube root 6)/(cube root 6)
= (cube root 6) x [(cube root 6)/(cube root 6)]
= (cube root 6) x [1]
= cube root 6

### wait what, i thought (4 *

wait what, i thought (4 * 3root6)^2 is 16root6...

### (4 x 3√6)² = (4 x 3 x √6)² =

(4 x 3√6)² = (4 x 3 x √6)² = (4)² x (3)² x (√6)² = 16 x 9 x 16 = 2304

### ((4*6^(1/3))^2)/ (2*2^1/3 * 4

((4*6^(1/3))^2)/ (2*2^1/3 * 4*3^1/3)
= 16*6^2/3 /2*2^1/3 * 4*3^1/3
= 2* 6^2/3 / 2^1/3 * 3^1/3
= 2

can you please tell me where i am making a mistake

### Everything is fine up to: 2*

Everything is fine up to: 2* 6^2/3 / 2^1/3 * 3^1/3 (second to last step)

However, 2^1/3 * 3^1/3 does not equal 6^2/3 (as your solution suggests).

The rule here is (a^n)(b^n) = (ab)^n

So, 2^1/3 * 3^1/3 = 6^1/3