Confusing Exponents Q

Question

can someone please explin thi to me. thanks

5^23 x 4^11 = 2 x 10^n

What is the value of n?

Thanks.

iamcartic · Answer

5^23 x 4^11 = 2 x 10^n

I guess the stem is not right???? Please check

in LHS: it sud be 4^12 or 5^21

buffdaddy · Answer

{5}^{23}* {4}^{11} = {2}*{10}^{n} 
-->  {5}^{23}*{2}^{22} = {2}*{5*2}^{n} 
--> =  {2}*{5}^{n}*{2}^{n} 
-->  {5}^{23}*{2}^{22} = {5}^{23}*{2}^{n+1}

hmmm its a dud question since n =23 but it doesn't workout properly

Vavali · Answer

I apologise

it's 5^21 x 4^11 = 2 x 10^n

jallenmorris · Answer

Then the answer is n = 21.

Explanation:

When you have exponents, you can multiply the base of the exponent ONLY IF THE EXPONENT IS THE SAME NUMBER!!

Example:  2^3 * 6^3 = 12^3

Furthermore, if you see that 4 is a multiple of 2, then you can make the base 2 rather than 4, but you must change the exponent or the value will be different. In this instance, you would double the value of the exponent from 11 to 22. because  4^{11} = 2^{22} .

This can be done with any perfect square of the base. (i.e.,  9^6 = 3^{12} ). Note that 9 is the square of 3. You could also do this with  27^3 = 3^9 .

So, now we have

5^{21} * 2^{22}

In order to make the exponent the same, pull out a 2. So we then would have
 5 ^{21} * 2 * 2^{21}  Now the base of 5 and 2 can be multiplied while keeping the same exponent. The result is:

2 * 10^{21}  n = 21.

gmatnub · Answer

n=21

The other posters showed the method.

buffdaddy · Answer

method with correct values

{5}^{21}* {4}^{11} = {2}*{10}^{n} 
-->  {5}^{21}*{2}^{22} = {2}*{5*2}^{n} 
--> =  {2}*{5}^{n}*{2}^{n} 
-->  {5}^{21}*{2}^{22} = {5}^{n}*{2}^{n+1}

n=21

jallenmorris · Answer

The others showed the method, but didn't really explain why some of the things work the way they do.

Confusing Exponents Q

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards