Do you know abc of algebra

$c^{z}$ = a

a = $c^{z}$

Since $b^{y}$ = c , then we can substitute in c into our equation, a = $c^{z}$ , so that we get

a = $(b^{y})^{z}$

And now, since $a^{x}$ = b , we can substitute b into our equation a = $(b^{y})^{z}$ , and get

a = $((a^{x})^{y})^{z}$

And through Exponent Rules, we can simplify and end up with

a = $a^{xyz}$

$a^{1}$ = $a^{xyz}$

$\boxed{1 = xyz}$

$\large b =a^x \\ \large c = b^y = (a^x)^y \\ \large a = c^z = (b^y)^z = ((a^x)^y)^z$

So we have $\large a = ((a^x)^y)^z = a^{xyz}$ .

Take the logarithm of both sides $\large \ln a = xyz\ln a \\ \large \dfrac{\ln a}{\ln a} = xyz \\ \large \boxed{xyz = 1}$

a^x =b

b^y=c

c^z=a

we can substitute a=c^z , c^{xz}=b

and again we can substitute b^y=c

then we get, b^{xyz}=b

If both bases are equal,then the powers also equal.

from that xyz=1 this is final solution.

If $abc=0$ , we have that $xyz$ is any number you like (except $0$ ), hence this problem does not have a unique answer. Everything would be alright, though, if the condition $abc\neq 0$ were added (Micah Wood's solution would follow).

a = c^z = b^(yz) = a^(xyz)
a = a^(xyz)
Therefore xyz=1 (Ans.)