Let’s first simplify the expression we want to evaluate. We see that [2^(1-x)]^2 can be simplified as (2 * 2^-x)^2 = 2^2 * 2^-2x = (2^2)/(2^2x)

Thus, if we can determine 2^2x, then we have an answer.

Taking the square root of both sides of the given equation, which is 2^4x = 3600 we have 2^2x = 60; thus:

(2^2)/(2^2x) = 4/60 = 1/15

Answer: B
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\(2^{4x} = 3600\)

\((2^{2x})^2 = 60^2\)

\(2^{2x} = 60\) .............. (1)

\((2^{1-x})^2 = \frac{2^2}{2^{2x}}\)

\(= \frac{4}{60}\).............. (From 1)

\(= \frac{1}{15}\)

Answer = B

Given 2^4x=1600
We need to find value of 2 ^(1-x)^2-------> Simplify this term

\((\frac{2}{2^x})^2\)

So we need to find value of \(\frac{4}{2^{2x}}\)

2^4x=3600. Taking a square root we get

2^2x=60

So we get 4/60 or 1/15
Ans is B

Similar question or practice:

given-2-4x-1600-what-is-the-value-of-154486.html#p1236720
if-4-4x-1600-what-is-the-value-of-4-x-161823.html
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Can someone please explain why we can't do the following:

Break 3600 to 2^4 x (3^2) x (5^2) --> so x=1

making the answer 1.

Why is this not the correct way to approach?

Thanks in advance

\(2^{4x} = 2^4*3^2*5^2\). If x=1, then you'd get that \(1 = 3^2*5^2\), which is wrong --> \(x \neq 1\). In fact from \(2^{4x} = 3600\) it follows that x is some irrational number (approximately 2.9534...), not an integer.
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2^(4x)= 3600 => x is just less than 3
=>2^((1-x))^2 = approx (2^(1-3))^2= approx 1/(2^4)
Hence B.
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GIVEN: 2^(4x) = 3,600
Raise both sides to the power of 1/2 to get: [2^(4x)]^(1/2) = 3,600^(1/2)
Simplify: 2^(2x) = 60

We want to find the value of: [2^(1−x)]²
To simplify, apply Power of Power law to get: 2^(2 - 2x)
This is equal to: (2^2)/[2^(2x)]
Replace 2^(2x) with 60 to get: (2^2)/60 = 4/60 = 1/15

Answer: B

RELATED VIDEO FROM OUR COURSE

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(2^1-x)^2 = 2^2/2^2x
so, (a^m)^n = a^(m*n) Right?
so (2^1-x)^2=2^((1-x)*2)=2^(2-2x)
now, a^(m-n)=(a^m)/(a^n) okay?
thus,
2^(2-2x) = 2^2/2^2x
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Sorry I want to ask my approach in this qn and why this may be or may not be right

So I first simplify the equation that we want to find out

2^2(1-x)
2^2/ 2^(2x) eq 1

then I want to find out how to solve this problem, but my approach is slightly not conventional (just my brain not thinking of square-root but okay, i want to ask participants here on this

so I saw 2^4x = 3600

meaning 2^4x = 2^4 x 3^2 x 5^2
in a way 2^4x = 2^2 (2^2 x 3^2 x 5^2)
then 2^4x = 2^2 (30^2)
then 2^4x/ 30^2 = 2^2 eq 2

So I put back the 2^2 to the eq 1

(2^4x/30^2) / 2^2x

2^2x / 30 x 1/2^2x = the 2^2x crossed out

so I got 1/30 instead---> can see where it goes wrong?

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