calculate large exponents

This topic has expert replies
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Tue Nov 28, 2017 9:14 am

calculate large exponents

by VINIYA » Tue Nov 28, 2017 9:21 am
How can I calculate (1.035)^ 12 very fast? any help is greatly appreciated.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Nov 28, 2017 9:33 am
VINIYA wrote:How can I calculate (1.035)^ 12 very fast? any help is greatly appreciated.
You wouldn't be required to perform this calculation on the GMAT.
Please post the entire question (with the 5 answer choices). It's possible that there's another approach that you've overlooked.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

subject hijinks

by Matt@VeritasPrep » Mon Dec 04, 2017 6:00 pm
To do it exactly we'd have to ask Shakuntala Devi! She'd be able to do it in a matter of seconds, but I don't know how. She wrote quite a few books on mental math, though.

I agree with Brent, we'd be best off estimating, but it'd still be tough. My rule of thumb is that (1 + small change) squared tends to be about 1 + 2*small change, so I'd work with that:

(1 + .035) * (1 + .035) ≈ 1.07

(1 + .07) * (1 + .07) ≈ 1.14

(1 + .14) * (1 + .14) ≈ 1.28

So 1.035 to the eighth gets us about 1.28. From there, we're looking at 1.28 (the eighth power) * 1.14 (the fourth power), so about 1.42. (The real answer is about 1.51, so you be the judge of whether this is close enough! The problem with this approximation is the more times you do it, the grosser the error becomes.)