Solve the equation. 16^6 times (1/4)^10x+8=64 times (4^x)^-5

Question

This is a college algebra problem for exponential functions

Answer 1

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16^6=16,777,216

(4^x)^-5=4^(x-5)

Answer 2

Replace exponents by conversion to powers of 2 and expand:

2^24/2^(20x+16)=2^6/2^(10x).

Start simplifying exponents (e.g., divide through by 2^6):

2^18/2^(20x+16)=2^(-10x).

Continue to work with exponents:

2^(18-20x-16)=2^(-10x).

Simplify and equate exponents:

2-20x=-10x;

10x=2, x=0.2.

CHECK:

16^6*(1/4)^10=64/4=16

2^24/2^20=16 OK!