Exponents from MGMAT CAT

[Ruben]

Hi,

I am finding hard to solve this exponential.

I know that 4^4x=1600 and I want to find what is the value of 4^((x-1)2)?

The solutions says that to obtain 4^((x-1)2) or 4^(2x-2), you need to square root
√(4^4x) = √(1600) wich gives 4^2x=40.

This is different from what the way I thought that I could simplify this type of exponents by doing 4^2*4^2x=1600 > 4^2x=100> 4^2x-2=100/16

The answer is 5/2 which I obtain if I square root both sides, but then on the left side I don't have the solution
asked by the problem anymore as it becomes √(4^2x-2). What am I doing wrong?

Help!!!

Thanks,

Ruben

[rfernandez]

by doing 4^2*4^2x=1600 ==> 4^2x=100 ==> 4^2x-2=100/16

That first line is where the error is. 4^2*4^2x is not equivalent to 4^(4x). You could rewrite 4^(4x) as 4^(2x)*4^(2x), or as [4^(2x)]^2. This last expression shows how taking the square root of both sides yields 4^(2x).

[Ruben]

Thanks Rey, that helps!

[Ruben]

One more question Rey,

How is 4^2*4^2x different from [4^(2x)]^2 ? What's the result of this mulitplication 4^2*4^2x ?

Thanks again!

Ruben

[RonPurewal]

How is 4^2*4^2x different from [4^(2x)]^2 ? What's the result of this mulitplication 4^2*4^2x ?

they are different in that the exponent of the left-hand expression is just '2', whereas the exponent of the right-hand expression is '2x'. since the two expressions are not identical, you can't write the overall expression as a perfect square. remember that squaring means multiplying together two exact copies of the same expression.

to figure out the results of calculations such as the one you're wondering about, you should use ANALOGIES TO KNOWN EQUATIONS - much easier than trying to memorize and apply abstract rules. think about the following equation:
(x^3)(x^5) = x^8
you can see that the exponents are added.
by the same token, then, (4^2)(4^2x) would be 4^(2 + 2x).

[Ruben]

Thanks Rey, now is perfectly clear!

[rfernandez]

Actually, that was Ron, but you're still welcome!