Question: Fraction with Products of Powers

Comment on Fraction with Products of Powers

Why do you not FOIL the numerator?
greenlight-admin's picture

FOIL only applies to the product of binomials in the form (a+b) or (a-b). For more on this, see:

In this question, we have the product of two products (not binomials). Try applying the FOIL method to (2x3)(5x5), and you'll see why it doesn't work with the product of two products)

Thanks for this FOIL explanation. Am learning a lot. I was an accounting students but little things like these I never knew. Thank God I am having to prepare for GRE before getting into my graduate program. It is really helpful. I thought it is too much to do all these before the your graduate program but I can see how important the GRE concept is. Thanks again GREENLIGHT TEAM. YOU ROCK
greenlight-admin's picture


I am not understanding the jump from 20x10^-40 to (2 x 10^1) x 10^-40. It's right there, but I can't see it. Thank you so much for this incredible program. I am grounding most of it!
greenlight-admin's picture

Thanks for the kind word, auroraflynn!

You're referring to the step that occurs at 1:25 in the above video.

When we're at the point where we have 20 x 10^-40, we should check the answer choices . . . that value is not there.

In fact, all of the answer choices are in the form 2 x 10^something

Given this, we might recognize that we can rewrite 20 as 2 x 10

Since 10 is the same as 10^1, we can write: 20 = 2 x 10^1

Once we replace 20 with 2 x 10^1, can then apply the Product Law to combine the 10^1 and the 10^-40 to get 10^-39

Does that help?


Hey Brent,

At this point, shouldn't we be able to divide 20 x 10^-40 by 10 to get the same result? However based on division of exponent rules, 20 x 10^-40/10 = 2 x 10^-41. Not sure what error I'm making here. Thanks!
greenlight-admin's picture

Hi Tatmanta,

At 1:25 in the above video, we see that the given expression evaluates to be 20 x 10^(-40).
In other words, (8 x 10^-16)(5 x 10^-20)/(2 x 10^4) = 20 x 10^(-40).
So, 20 x 10^(-40) is the correct answer. The only problem is that this is not among the answer choices.
This means we need to find an EQUIVALENT way to express 20 x 10^(-40)
If we divide this value by 10, then our answer becomes 1/10 of what it should be.
This makes no sense, since 20 x 10^(-40)/10 is not equivalent to 20 x 10^(-40)

Here's an analogous example.
Let's say we want to evaluate 30 x 5.
We perform the necessary multiplication to get: 30 x 5 = 150
From here, let's divide 150 by 10 to get 15.
This is no good because 15 is not equal to 150.

Does that help?

This is likely very simple, but why does (8 * 10^-16)(5 * 10^-20) simplify to 40 x 10^-36? Is this using associative property?
greenlight-admin's picture

The associative property for multiplication says (ab)(cd) = (ac)(bd) [among other things]

So, we can write: (8 x 10^-16)(5 x 10^-20) = (8 x 5)(10^-16 x 10^-20)
= (40)(10^-36)

Does that help?


Yes, thank you. Just wanted to be sure I hadn't missed something.
greenlight-admin's picture

Good idea. It's always better to confirm your hunches than to wonder if you're making the right assumptions.


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