SOLUTION: I am currently working on the question (8x)^(-1/2) = 1/4. The answer that I keep getting is that it is 4/3. This is an example of what I have been doing. 2^(3x(-1/2)) = 4^(-1) 2

Question 247433: I am currently working on the question (8x)^(-1/2) = 1/4. The answer that I keep getting is that it is 4/3. This is an example of what I have been doing.
2^(3x(-1/2)) = 4^(-1)
2^(-3x/2) = 2^(-2).
-3x/2 = -4
x = 4/3
Could you please let me know where I am going wrong? The answer says that it is 2, but I'd really like to know how I'm going wrong. Thank you for your time,
Robyn
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
(8x)^(-1/2) = 1/4. The answer that I keep getting is that it is 4/3. This is an example of what I have been doing.
2^(3x(-1/2)) = 4^(-1) ** 2^3*x^(-1/2) ..... You included the x
2^(-3x/2) = 2^(-2).
-3x/2 = -4 **** The exponents are equal, so -3x/2 = -2
x = 4/3
------------
Do it like this:
(8x)^(-1/2) = 1/4
Multiply thru by (8x)^1/2
1 = sqrt(8x)/4
sqrt(8x) = 4
Square both sides
8x = 16
x = 2

RELATED QUESTIONS
HELP! I have been working on this for a long time and keep getting wrong answers. I... (answered by ewatrrr)

Ahhhh, I am a pretty good math student and this question is probably not something I will (answered by Edwin McCravy)

How do we simplify 8 to thee 1/3 power? This is the problem I am currently working on so... (answered by vasu2qute)

The problem that I am working on is this one: 1/a-b + 4/b-a -8/a+b - 11a-5b/b^2-a^2 I... (answered by josmiceli)

the question is find the quotient using long division the problem is 3x^3+2x^2-19x+1 (answered by richwmiller)

I would like it if someone could show me step by step with an explaination on how to... (answered by glabow)

What is the equation of the line that passes through (4, -1) and (-2, 3)? Can you... (answered by Alan3354)

I am stuck on a question about exponential expressions and the order of operations. I... (answered by jim_thompson5910)

I'm not sure what type of equation this is, but I need help on how the answer was found. (answered by drk)