Simplify the expression 2^4x = 64, I know the answer but I can't show my steps?

When you want to solve fastly, you can use the method of changing to same base.
(2^4)^x=64
(16)^x=64
(16)^x=(16)^(3/2)
x=3/2

Use base 2 is easier than base 16
2^(4x)=64
2^(4x)=2^(6)
(4x)=(6)
x=6/4
x=3/2

Standard solve I use logarithmic (for such as not same base)
2^(4x)=64
log(2^(4x)) = log(64)
4x*log(2) = log(64)
4x*log(2) = log(2^6)
4x*log(2) = 6*log(2)
4x=6
x=6/4
x=3/2

2^(4x) = 64

To solve, just change the 64 to 2^6
2^(4x) = 2^6

Since the bases are equal, they're both 2, you can set the exponents equal to each other
4x = 6

Divide both sides by 4
x = 6/4

Reduce and the answer is
x = 3/2 or 1.5

[-2(x^2-3)^-3 (2x) (x+a million)^3 - 3(x+a million)^2 (x^2 - 3)^-2] / [(x+a million)^3]^2 = [-4x(x^2 - 3)^(-3)(x+a million)^3 - 3(x+a million)^2 (x^2 - 3)^(-2)] / [(x+a million)^3]^2 = {(x^2 - 3)^(-3)(x+a million)^2[-4x(x + a million) - 3(x^2 - 3)]} / [(x+a million)^3]^2 = {(x^2 - 3)^(-3)[-4x^2 - 4x - 3x^2 + 9)]} / (x+a million)^4 = (-7x^2 - 4x + 9) / [(x+a million)^4 (x^2 - 3)^3]

Not sure about your presentaion. Is it :-
Question 1
(2^4) (x) = 64
16 x = 64
x = 4
or
Question 2
2^(4x) = 64
4x log 2 = log 64
4x = log 64 / log 2 (logs to base 2)
4x = 6
x = 3/2

2^(4x) = 64
2^(4x) = 2^6

4x = 6
x = 6/4
x = 3/2 (1.5)

2 to the power 4x is 64. Now we know that 2 to the power 6 is 64. So 4x is equal to 6. Or x ==6/4 =1.5.
Hope this helps.

nevermind

2^4x=64 = 2^6
4x=6
x=3/2

(2 x 2 x 2 x 2) ^x = 64

2^4x=64
16x=64
(div. 16= div. 16)
x= 4