Exponent Rules

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

somail: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Tue Jul 01, 2008 11:54 am; Location: San Diego

Exponent Rules

by somail » Thu Aug 28, 2008 12:13 pm

How is the following simplification done:

2^100-2^96
2^96*(2^4-1) (This is the step I do not get)
2^96*(16-1)
15*2^96
2^96*3*5.

How is 2^11 turned into 2^(4-1) and then multiplied against 2^96? Is there a general rule?

thanks

Quote

Source: Beat The GMAT — Problem Solving | Thu Aug 28, 2008 12:13 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: Exponent Rules

by Stuart@KaplanGMAT » Thu Aug 28, 2008 12:27 pm

somail wrote:How is the following simplification done:

2^100-2^96

We can only add or subtract in these situations if the base is the same AND the exponent is the same.

For example, we can solve:

5(x^5) - 2(x^5) = 3(x^5)

However, there's no simple solution for:

5(x^5) - 2(x^3)

So, if we're faced with a situation in which the bases are the same but the exponents aren't, we need to find a common exponent. We do so through factoring.

Let's look at the original question:

2^100 - 2^96

To get the same exponent, we need to reduce 2^100.

We can rewrite 2^100 as (2^4)(2^96) = 16(2^96).
We can rewrite 2^96 as 1(2^96).

So, we can rewrite 2^100 - 2^96 as:

16(2^96) - 1(2^96) = 15(2^96)