Can you solve this "Properties of Exponents" quest

[EbrahimHashem]

Which of the following is equal to 5^17 X 4^9?

A. 2 X 10^13

B. 2 X 10^17

C. 2 X 10^20

D. 2 X 10^26

E. 2 X10^36

[truplayer256]

5^17*4^9

5^17*(2^2)^(9)

5^17*2^(2*9)

5^17*2^18

5^17*2^17*2

(5*2)^(17)*2=(10)^(17)*2 B.

[EbrahimHashem]

5^17*4^9

5^17*(2^2)^(9)

5^17*2^(2*9)

5^17*2^18

5^17*2^17*2

(5*2)^(17)*2=(10)^(17)*2 B.

Can you please explain the bolded step?

[mygmat.2009]

5^17 * 4^9

(rewrite the 5 to 10/2 and the 4 to 2^2)

==> (10/2)^17 * (2^2)^9

==> ( (10^17) / (2^17) ) * (2^18)

==> (10^17) * (2^18) / (2^17)

==> (10^17) * 2

==> B

[truplayer256]

truplayer256 wrote:
5^17*4^9

5^17*(2^2)^(9)

5^17*2^(2*9)

5^17*2^18

5^17*2^17*2

(5*2)^(17)*2=(10)^(17)*2 B.


Can you please explain the bolded step?

5^17*2^17*2

Whenever you have bases with common exponents, you can always combine them into one base with a common exponent. In this case, we have the common exponent 17 and the bases 5 and 2, so we can combine 5 and 2 into (5*2)^(17) or (10)^(17) since this is the same thing as 5^17*2^17.

[EbrahimHashem]

Thanks, that was helpful

[Stuart@KaplanGMAT]

Which of the following is equal to 5^17 X 4^9?

A. 2 X 10^13

B. 2 X 10^17

C. 2 X 10^20

D. 2 X 10^26

E. 2 X10^36

Some solid algebraic explanations, but let's get into the thinking of the question as well and see how we could have avoided almost 100% of the math.

Step 1 of the Kaplan Method for PS: study the Q and the answers.

Many people foolishly ignore part 2 of this step; remember, on a multiple choice test the answer can be your best friends in the world.

Here, we see that all the choices are written as powers of 10. Further, there's an extra 2 in each choice. So, what's our task? Restate the orginal expression as a (2 * power of 10).

We know that 10 has two prime factors, 5 and 2. Accordingly, for each 5 and 2 we have, we can make one 10.

Let's look at the original expression:

5^17 X 4^9

The 5 is already pulled out for us - we know there are 17 of them. From 17 5s, you can make exactly 17 10s.

Now remember back to step 1, when we studied the choices? Each choice was 2 * power of 10. There were no extra 5s! Therefore, all 17 of those 5s must get used up.

Accordingly, the only possible answer is 2*10^17... choose B.

Here's something really important to remember for people shooting for 720+ scores... the difference between 700 and 800 is not how good you are at doing math - it's how good you are at not doing math.