Need some help with this.

Question

Answer 1

y and z are exponents. x is the base

exponents multiply, keeping the base the same

(x^y)^z = (x^z)^y

but

(x^y)^z doesn't equal (y^x)^z (at least not often) because you can't switch a base with an exponent

2^3 = 8, but 3^2= 9. the base and its exponent are not interchangeable. But an exponent and an exponent are interchangeable. If one is the exponent of the other.

try a simple example: x=2, y=4, z=1/2

(2^4)^(1/2) = 16^1/2 = 4

(2^1/2)^4) = (sqr2)^4 = 2^2 = 4

but

(2^4)^(1/2) = 4

and

(4^2)^(1/2) = 4

still, not always true,

try x=1, y= 2, z=3

(1^2)^3 = 1

(1^3)^2 = 1

but

(2^1)^3 = 8 which doesn't equal (1^2)^3 = 1^6 = 1