Respuesta :

MisterBrian

Answer:

1

Step-by-step explanation:

Correct question:

If a=b^x, b=c^y and c=a^z, then what is the value of xyz? (Bolded part)

Given: a = b^x ...(1)

  • b = c^y ...(2)
  • c = a^z ...(3)

Putting the value of b from (2) onto eqn (1),

  • a = (b)^x = (c^y)^x = c^xy ...(4)

Putting the value of x from eqn (3) to (1):

  • a = (c)^xy = (a^z)xy = a^(xyz)

Since the bases "a" are equal,the powers are equal:

By the base law of indices:

  • a¹ = a^(xyz) => xyz = 1

[tex]\boxed{\sf xyz = 1}[/tex]