If 4^4x = 1600 then what is the value of 4^(x-1)2 ?

Hi Pritam 4^4x = 1600 4^2x = root(1600) = 40.... (1) We need to find 4^(x-1)2 = (4^2x)/ (4^2) Substituting (1), we get = 40/16 = 2.5 ANS 2.5

4^2x=|root(1600)| and how you get 400? 400^2=160000 and 4^(x-1)2 is meant to be 4^(x-1)^2 - We don't factor by 2 at the end of exponential expression I have edited my post above. Root(1600) = 400 was a blunder on my part. . It should be 40. Regarding expression "4^(x-1)2 ", it cannot possibly be "4^(x-1)^2" in this question as it would yield no result. The proper interpretation is given below: 4^(x-1)2 = [4^(x-1)]^2 or 4^2(x-1)

4^2x=|root(1600)| and how you get 400? 400^2=160000 and 4^(x-1)2 is meant to be 4^(x-1)^2 - We don't factor by 2 at the end of exponential expression das.ashmita wrote:Hi Pritam 4^4x = 1600 4^2x = root(1600) = 400.... (1) We need to find 4^(x-1)2 = (4^2x)/ (4^2) Substituting (1), we get = 400/16 = 25 ANS 25

pritam.ryders wrote:If 4^4x = 1600 then what is the value of 4^(x-1)2 ? the required is 4^(x-1)^2 along with 4^(x^2-2x+1) or (4^(x-1))^2 ?? I hope the latter is our needed condition, as with 4^(x-1)^2 we fall to the given 4^4x=1600, 4^2x=|40| and 4^2x=|4*10| and consider positive case first, 4^(2x-1)=10. From the above expression we have an exponent (x^2-2x+1) and we can rewrite 4^(2x-1)=10 as 4^(-2x+1)=1/10. So we have 1/10 * 4^(x^2) where 4^(x^2) is unknown. If are given (4^(x-1))^2, then 4^(2x-2) is sought for solution. Since 4^(2x-1)=10, 4^(2x-2)=10/4=2.5

pritam.ryders wrote:If 4^4x = 1600, then what is the value of (4^(x-1))² ? 40 20 10 5/2 5/4 Rephrase (4^(x-1))² into a form resembling 4^4x: (4^(x-1))² = 4^(2x-2) = (4^2x)/4² = (4^2x)/16. Use 4^4x = 1600 to determine the value of 4^2x: 4^2x = (4^4x)^(½) = 1600^(½) = 40. Substitute 4^2x = 40 into (4^2x)/16: (4^2x)/16 = 40/16 = 5/2. The correct answer is D.

But Mitch with your notation, 4^(x-1)^2 falls into 4^(x^2-2x+1) should not this be (4^(x-1))^2 by squaring the entire expression?

pemdas wrote: Should not this be (4^(x-1))^2 by squaring the entire expression? Yes, indeed. The problem asks for the value of (4^(x-1))². I've corrected the notation in my post above.