Lesson: Exponent Laws - Part I

Comment on Exponent Laws - Part I

Very informative. In school my teach just said that a number to the power of zero always equals 1 but I never knew WHY. THanks!

Great Math videos!!!
Really helpful.

https://greprepclub.com/forum/a-googol-is-the-number-that-is-written-as-1-followed-by-2900.html

To solve this question I used the following approach:
1) 100,000/8 = 12,500
2) 100,000/5 = 20,000
3) 100,000/4 = 25,000
4) 100,000/2 = 50,000

The sum of their values comes to 22. What is wrong with this approach?
greenlight-admin's picture

Question link: https://greprepclub.com/forum/a-googol-is-the-number-that-is-written-as-...

One problem is that 100,000 does not equal a googol.

We're told that "A googol is the number that is written as 1 followed by 100 zeros."
So, a googol = 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

That said, your approach will also work. HOWEVER, you didn't read the question as it is intended.
We're asked to find the sum of the digits of the SUM of G/8 + G/5 + G/4 + G/2
In your case, the SUM = 12,500 + 20,000 + 25,000 + 50,000 = 62,500

Sum of digits = 6 + 2 + 5 + 0 + 0 = 13 (the correct answer)

Cheers,
Brent

In this case, we add all the digits 1 + 0 + 7 + 5 + 10000... should we add the 1 because it is 10^97?
greenlight-admin's picture

Sorry, but I'm not sure what you're asking. Which question are you referring to?

https://greprepclub.com/forum/a-googol-is-the-number-that-is-written-as-1-followed-by-2900.html
Thank you ;)

greenlight-admin's picture

Be careful, we're not calculating the SUM (1075) + (10^97)
We're calculating the PRODUCT (10^97)(1075)
[aside: if we WERE calculating the sum, you'd be correct about adding an additional 1]

Notice that (10^1)(1075) = 10750 (sum of digits = 13)
And (10^2)(1075) = 107500 (sum of digits = 13)
And (10^3)(1075) = 1075000 (sum of digits = 13)
And (10^4)(1075) = 10750000 (sum of digits = 13)
And (10^5)(1075) = 107500000 (sum of digits = 13)
.
.
.
etc

So, it must be the case that the sum of the digits of (10^97)(1075) is 13)

Does that help?

Cheers,
Brent

Thank you Brent.

I used only 100,000 as i identified a pattern that after 10,000 or even 1000 the remaining integers will be zero, so no point in adding them. My mistake here was to add the digits individually: 12500 + 20000 + .... = 22
I should had summed it up and then added the digits.

Any tips for avoiding silly mistakes? It's simply killing me at the moment.
greenlight-admin's picture

I figured that's what you were doing :-)

Silly mistakes can kill one's score. Here's an article on how to avoid that: https://www.greenlighttestprep.com/articles/avoiding-silly-misteaks-gre

Cheers,
Brent

https://greprepclub.com/forum/units-digit-of-n-in-comparison-of-2769.html#p29004

Can we solve this through prime factorization?
greenlight-admin's picture

Question link: https://greprepclub.com/forum/units-digit-of-n-in-comparison-of-2769.htm...

Since all we care about is the units digit of n, finding the prime factorization of each value won't really help in this question.

Hi, in the following question, please can you explain how in this method, she gets the answer.

https://greprepclub.com/forum/qotd-12-if-t-is-an-integer-and-8m-16-t-which-of-the-fo-2629.html

Here 8m = 16^t or m = 16^t/8 but this is not equal to 2t.

Say t = 2 and m = 16^2/8 = 256/8 = 32

So if m = 2t, should be m = 2 × 2 = 4

Thank you :)
greenlight-admin's picture

Question link: https://greprepclub.com/forum/qotd-12-if-t-is-an-integer-and-8m-16-t-whi...

Sandy (the poster you're referring to) is explaining why answer choice A is incorrect.

Answer choice A suggests that, if 8m = 16^t, then m = 2^t
In other words, if m = 16^t/8, then m = 2^t

Sandy goes on to test a value of m to see whether A is the correct answer.
If t = 2, then m = 16^t/8 = 16^2/8 = 256/8 = 32
Conversely, if t = 2, m = 2^t = 2^2 = 4

This tells that the equations m = 16^t/8 and m = 2^t are NOT equivalent.
Therefore, the correct answer cannot be A

Does that help?

Cheers,
Brent

Yes, thank you :D

Hi! Why do we keep the t?
greenlight-admin's picture

The question asks us to "expresses m in terms of t"
So, once we determine that m = 2^(4t - 3), we have our answer.

Hi! I mean, I understand 16 = 2^4, however I am not sure what the "t" represents. Does it simply represent 1?
greenlight-admin's picture

t doesn't represent a single value; it can have infinitely many values (as long as those values, along with m, satisfy the equation 8m = 16^t)

For example, one solution to the equation is m = 2 and t = 1
To verify the solution, substitute to get: 8(2) = 16^1.
It works.

Another solution to the equation is m = 32 and t = 2
To verify the solution, substitute to get: 8(32) = 16^2.
It works.

And so on.

In general, we can say that all solutions to the original equation will be such that m = 2^(4t - 3)
So, for example, if t = 3, then m = 2^(4(3) - 3) = 2^9 = 512
So, another solution to the equation is m = 512 and t = 3

Does that help?

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