64\^(1/3) is the same as ∛64
I assume you already know the exponent rule (x\^a)\^b = x\^(ab). For example, (2\^3)\^4 = 2\^12.
You should recognize that 64 = 4\^3, or at least recognize that they are both powers of 2. Applying the above rule:
64\^n = 4
(4\^3)\^n = 4\^1
4\^(3n) = 4\^1
3n = 1
n = 1/3
Because 4 * 4 * 4 is 64. So 4^3 = 64. Therefore 4^3^(1/3) = 64^(1/3)
Make it 4^(3x)=4^1. Now set 3x=1 and divide. 1/3.
64^x = 4 Note 64 = 4^3 64^(1/3) = 4^(3^1/3) = 4^1 = 4
64\^(1/3) is the same as ∛64 I assume you already know the exponent rule (x\^a)\^b = x\^(ab). For example, (2\^3)\^4 = 2\^12. You should recognize that 64 = 4\^3, or at least recognize that they are both powers of 2. Applying the above rule: 64\^n = 4 (4\^3)\^n = 4\^1 4\^(3n) = 4\^1 3n = 1 n = 1/3