Simplifying the equation we get:
√b/a x √c/b x √a/c = 1 (if -1 is the exponent, the it is equal to the reciprocal of the base. Eg. a^-1 = 1/a)
Squaring both sides of the equation:
(√b/a x √c/b x √a/c)² = (1)²
On Simplifying we have:
b/a x c/b x a/c = 1
All the the values cancel each other out leaving 1:
b/a x c/b x a/c = 1
Therefore, 1 = 1
Hence, proved.