PSAT's

[Hellfighter 17]

Originally posted by Android 20
Can someone please explain some of these messed up exponential properties to me? I got a question wrong and still stand behind it, because the "correct" answer still seems like a load of bullshit to me.

Here was the question:

Simplify this Expression:

5^X * 2^(X+Y)

I said the answer was 10^(2X+Y) due to the additive property of exponents, but they claim the answer was 10^X * 2^Y.

If you aren't sure about an answer with variables, give the variable(s) /a value(s) and work it out. I'm assuming "^" is "to the power of."

5^X * 2^(X+Y)
= 5^2 * 2^(2+3)
= 25 * 2^(5)
= 25 * 32
= 800

You simplified expression:

10^(2X+Y)
= 10^[2(2)+3]
= 10^(4+3])
= 10^7
= 10 000 000

Their simplified expression:

10^X * 2^Y
= 10^2 * 2^3
= 100 * 8
= 800

With the original expression [5^X * 2^(X+Y)] you have to recognize that 5 is being multiplied by 2. And it's saying that 2 to a certain power is being multipled by 5 to a certain power. The powers are the same, so you can think of it just like 5^1 * 2^1, which would be 10^1, so that would be 10^X. But, you still had 2 to the power of Y, and since X and Y were added, you can simply just take the X out and leave a 2 ther,e leaving you with 10^X * 2^Y.

But, I am not a certified professor, so. . .