A = (0.82)^2 (0.82)^3, B = (0.82)^6: which is bigger, or can

[leylan]

Hi Folks,
I'm studying to take the GRE's right now and struggling to remember all my high school math (4 years feels like a long time :? ). Most of it is okay so far, but I was having difficulty with a couple of the practice problems I was doing, and even though these aren't actual test questions, thought it'd be good if someone explained how the concepts worked.

The first problem was:

Column A : (0.82)^2(0.82)^3
Column B : (0.82)^6

(choose one)
1. Column A is larger
2. Column B is larger
3. Both the same value
4. Cannot be solved with the information given.

The second problem was:

For all real numbers a, let a^*=1-a
Column A : ((-1)^*)*
Column B : 2^*

(same here; choose one)
1. Column A is larger
2. Column B is larger
3. Both the same value
4. Cannot be solved with the information given.

Thanks in advance for any help anyone can provide. I usually can figure out exponents and variable problems (although I have no idea what the deal with * is in the second problem), but these really threw me for a loop.

 

[Denis]

Re: Exponents and variable confusion

Column A : (0.82)^2(0.82)^3
Column B : (0.82)^6

rule: a^x times a^y = a^(x + y)
so (0.82)^2(0.82)^3 = .82^5

.82^5 is larger than .82^6, since .82 < 1 ; like .5 * .5 = .25 ; .5 * .5 * .5 = .125

For all real numbers a, let a^*=1-a
Column A : ((-1)^*)*
Column B : 2^*

That's a real "brain fryer" leylan!

Col A: do inside brackets first: (-1)^* = 1 - (-1) = 1 + 1 = 2
So we're now at (2)^*
Hey, we're lucky cause that's same as Col B : so they're equal :idea:

 

[mmm4444bot]

Re: Exponents and variable confusion

... For all real numbers a, let a^*=1-a

... I have no idea what the deal with * is ...

Hello Leylan:

The ^* operator is defined by their equation above.

In this definition, the ^ symbol no longer denotes exponentiation.

When any real number is followed by the ^* operator, it means "subtract the real number from 1".

8^* = 1 - 8

(44/7)^* = 1 - 44/7

[-sqrt(2)]^* = 1 + sqrt(2)

and so on ...

This is why Denis wrote (-1)^* equal to 1 - (-1).

Column A : ((-1)^*)*

I hope the second asterisk above is a typographical error, since they did not define (a)*.

I read it as ((-1)^*)^*

Cheers,

~ Mark

 

[leylan]

Re: Exponents and variable confusion

Wow, okay, those are both making a lot more sense now, especially with mmm4444bot's explanation. Thanks a lot guys!