If a=10x and b=10y , (aybx)z , then what is the value of xyz?

Question

This is from indices of grade 11.

Answer 1

z has not been defined in terms of anything else. Here are two interpretations of a and b:

(1) a=10x, b=10y, so x=a/10 and y=b/10, making (axby)z=(a²b²)z/100;

(2) a=10^x, b=10^y, so x=log₁₀(a), y=log₁₀(b), making (axby)z=abzlog₁₀(a)log₁₀(b).