z=3/8
Step-by-step explanation:
Step by step summary
We have to remember some of these basic indices’ corollary
- (1/a)ⁿ = (a)⁻ⁿ
- (a²)ⁿ = (a)²ⁿ
- (a)ᵇ.(a)ⁿ = (a)ᵇ⁺ⁿ
Using these corollaries we would proceed with the problem
(1/4)^(3z-1)= (4)^(1-3z) using 1 theorem
Similarly
(16)^ (z+2)= (4)^(2(z+2)) using 2nd theorem
(64)^ (z-2)=(4)^ (3(z-2)) using 2nd theorem
Solving above 2 equations we get
(4)^(2z+4). (4)^(3z-6)
(4)^(2z+4+3z-6) using 3rd theorem
(4)^(5z-2)
Thus, we get the equation
(4)^(1-3z) = (4)^(5z-2)
Since the bases are the same we could equate the powers
1-3z=5z-2
8z=3
Z=3/8
