Question

If a = b^x, b = c^y, c = a^z, then the value of 8 xyz is ______.

Options

• 1

• 2

• 4

• 8

Answer 1

If a = b^x, b = c^y, c = a^z, then the value of 8 xyz is 8.

Explanation:

From the given,
a = b^x

b = c^y

c = a^z

Substituting (b = c^y) into the first equation:

a = (c^y)^x

a = c^xy

Then substituting (c = a^z) into this:

a = (a^z)^xy

a = a^zxy

This shows:

a = a^xyz

So, for (a ≠ 0, 1), the exponents must be equal:

1 = xyz

Considering the problem involves (8xyz), the natural extension is:

8xyz = 8 × 1

8xyz = 8

Hence, the value of 8xyz is 8.