Sign in
Please select an account to continue using cracku.in
↓ →
CAT WhatsApp Group
If $$m$$ and $$n$$ are natural numbers such that $$n > 1$$, and $$m^n = 2^{25} \times 3^{40}$$, then $$m - n$$ equals
We must bring the right-hand side in the form so that everything has the same power.
25 has factors 1, 5 and 25
The only common factor 40 and 25 have is 5 (other than 1 of course, which does not work)
So the right-hand side can be rewritten as $$\left(2^5\right)^5\times\ \left(3^8\right)^5$$
$$\left(32\times\ 81\times\ 81\right)^5$$
$$\left(209952\right)^5$$
Giving the value of m - n as 209952 - 5 = 209947
Therefore, Option D is the correct answer.
Was this solution helpful?
Click on the Email ☝️ to Watch the Video Solution
Create a FREE account and get:
Book Free CAT Mentorship
Get personalized CAT strategy from a 99%iler
500+ students mentored
OTP Verification
Enter the 6-digit code sent to your phone
Booking Summary
Enter OTP
Didn't receive the OTP?
Start your IIM journey with the right preparation and crack CAT 2026.
Educational materials for CAT preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.
91- 6303239042
