Question

Prove that
(z^a/z^b)^c * (z^b/z^c)^a * (z^c/z^a)^b =1

Answer 1

Explanation:

remember, when we multiply the same base, we add the exponents, when we divide the same base we subtract the exponents.

when we have exponent of exponent, we multiply the exponents.

so,

the expression is

(z^ac / z^bc) × (z^ab / z^ac) × (z^bc / z^ab) = 1

we have in there the commutative and associative properties of multiplication : the sequence of operands do not matter at all.

and therefore we have in there the terms :

z^ac / z^ac

z^bc / z^bc

z^ab / z^ab

all three are 1

and so the main expression is

1 × 1 × 1 = 1

which is true, of course, and therefore the original equation is true.