Please refer to my explanation above.

B is -64 for instance and A is -27

On the number line (negative side) -64 is farthest from zero than -27.

Quantity B is NOT \(4^x\) but - \(4^x\)

Therefore, A is the answer. A is always > B

Hope this helps

Plz Clarify -

"2^{2x} becomes -4^x and -4 raised to odd integer power is always negative: -4^1 = -4 ; -4^3 = -64"

Now if I consider this way will it be wrong-

x=1

In B;

-2^{2x} = -2^{2.1} [since x=1]

=-2^{2} [2.1 = 2] = +4

Sorry but in this scenario, the rules for powers teach us that what you said leads to the wrong solution.

You must before multiple -2*2 = -4 the rise \(-4^x\).

Hope this helps

regards

(-2)^x is not the same as -2^x.

Official Explanation

In Quantity A, a negative integer is raised to a positive odd power. Odd powers retain the sign of the underlying quantity. Thus, (−3)x = −3x. Meanwhile, in Quantity B, the exponent may be broken up as follows, so as to match that in Quantity A: - \(2^2x\) = − (\(2^2\))^x = − \(4x\). Note that the minus sign is applied after the multiplication, for both quantities. Both columns are negative;

A) \(-3^x\)

B) \(-4^x\)

However, for positive x, \(3^x < 4^x\), so that

- \(3^x\) > - \(4^x\). Therefore Quantity A is larger.

Watch this
https://www.youtube.com/watch?v=YLuLpmjOFYw

Answer: B
x is odd, thus (-3)^x is negative.
-2^2x, because 2x is even, -2 to power of an even value is positive.
So B is bigger than A
*also we can thick ofB as: (-2^2x) = ((-2)^2)^x = 4^x which is positive.

People fell in the trap of not comprehending Quantity A: - 2^2x = − (2^2)^x = − 4x.

If the answer to this is B, this question was not properly written. According to PEMDAS, powers get precedence and 2x will always be even (rule of even x odd = even). Hence, any negative number raised to an even positive power will always be positive.

Also, what I can see you people who say A is greater do is square -2 before applying the odd value of x which is never correct mathematically. Treat 2x like they are in a bracket before applying to -2 to get your answer.

you are absolutely right.

However, \(-2^{2x} = -(2^2)^x = -4^x\)

Hope this helps

Even after reading all these discussion, I do not understand this.

If x=1, A = -3 and B= +4. How is the answer A then? I think the answer should be D

If x = 1, the A= -3 and B = - 4

Hope this helps

Answer: B
A: x is odd, thus -3 in power of something odd is negative.
B: x is odd, but it is not important because power of -2 is 2x which is always even. So B is a positive value.

I think the question is really misleading but do such questions appear on the test? I do not understand why are we taking -2^2x as -4^x. It can also be thought of as (-2)^2x. In this case, B will be greater.

There is a catch in this problem

If we look at statement 1 we have
\((-3)^x\)

now any odd value of x it will be negative with multiples of 3.

Now for statement 2;

we have

-\(2^{2x}\)

Now the negative sign will always be present since we are not squaring the sign as it is not under bracket as in statement 1.

Therefore any odd values of x in equation 2 will always be less than the value in equation 1

So the way I approached this was by doing a guess and check method.

The values for 'x' used: 1, 2, -1. -2

x = 1 --> (-3)^1 = -3 & -2^2(1) = -4 ---> -3 > -4
x = 2 --> (-3)^2 = 9 & -2^2(2) = -16 ---> 9 > -16
x = -1 --> (-3)^(-1) = -1/3 & -2^2(-1) = -1/4 ---> -1/3 > -1/4
x = -2 --> (-3)^(-2) = 1/9 & -2^2(-2) = -1/16 ---> 1/9 > -1/16

Based on the calculations we completed, it is absolutly clear that the answer is A.