Exponents strategy question

[nm37]

Hi folks,

I just started my GMAT prep a few days ago -- I'm on MGMAT Strategy Guide 1 - Number properties -- and I'm stuck on an example located on page 68.

The guide displays the following rule and example:

Rule - a^x * b^x = (ab)^x
Example given - 12^5 = 2^10 * 3^5

I don't get it. I have two different bases and exponents. How do they come together to form 12^5?

I apologize if I'm missing an obvious step, my brain is pretty drained at the moment.

Thanks in advance!

[kyle_proctor]

This is the step you are missing:

2^10 = 4^5

This is two different ways to say the same thing...


Remember 4 = 2^2 and (2^2)^5 = 2^10


4^5 x 3^5 = 12^5

Hope that helps

[bineeshnair4u]

Hi folks,

I just started my GMAT prep a few days ago -- I'm on MGMAT Strategy Guide 1 - Number properties -- and I'm stuck on an example located on page 68.

The guide displays the following rule and example:

Rule - a^x * b^x = (ab)^x
Example given - 12^5 = 2^10 * 3^5

I don't get it. I have two different bases and exponents. How do they come together to form 12^5?

I apologize if I'm missing an obvious step, my brain is pretty drained at the moment.

Thanks in advance!

First of all.. this question doesnt belong here.. I guess someone will come and block this..

Here is how it works

if u can write a^x * b^x = (ab)^x then vice versa is also true

The example is 12^5 = (4*3) ^ 5
we know that (ab) ^ x = a^x * b^x
so (4*3) ^ 5 = 4^5 * 3^5 ----------> (1)
again 4^5 = (2^2)^5 = 2^(2*5) = 2^10
Rule: (a^x)^y = a^(xy)
so substituting back to expression (1) we get
(4*3) ^ 5 = 2^10 * 3^5

Hope this helps.. :)

[nm37]

The book must have a typo, I guess. Thank you for the explanation!

This is the step you are missing:

2^10 = 4^5

This is two different ways to say the same thing...

Remember 4 = 2^2 and (2^2)^5 = 2^10

4^5 x 3^5 = 12^5

Hope that helps!

[jnelson0612]

Thanks Kyle! :-)