Math Exponent question. Show me your Skills!!

[MikeT]

I was asked by someone here in my office how to raise a number to a fractional exponent. say 3 to the 2/3 power. They will be taking a test on this on Saturday and they are NOT ALLOWED to use a calculator with a y to the x button on it which would make this a one step process. BTW 3 to the 2/3 power is 2.08 when using the fancy key on my calculator.

My question is, how can this be solved using a regular calculator?? There must be a way.

Any math people out there??

 

[biglou]

Short answer: it's the cube root of 3, squared. (3 to the .667 power).

My first guess was wrong. I guessed 3 to the 1/3 power (or it's cube root) time 2. Close, but not quite.

edit:removed "squared" from the end of the first line.

 

[2strokerfun]

Lord I thought I remembered this. Until I started doing the math. What you are trying to find is the cube root of 3 squared. The top of the fraction is the power and the bottom of the fraction is the root (if I remember correctly). So, you find the cube root of 3 (1.44224...) and multiply it by itself. The problem with this particular equation is the cube root of 3 is kind of like pi, it goes on and on and on and on.

 

[Patman]

Man I like pie.

Pi Day is just around the corner!

 

[flyingfuzzball]

big lou nailed it. we just did this in math today.

here's another exponent question that i had on a test a couple days ago.

what is the remainder when 3^0+3^1+3^2...3^2009 is divided by 8?

A) 0
B) 1
C)2
D)4
E)6

no calculator is allowed though that doesnt matter. it has something to do with patterns but me and my friends couldnt figure it out.

this question was on the AMC 10 test. it is ridiculously hard.

 

[biglou]

That's a good one, and I thought I had the answer, but I was dividing by 9 instead of 8. If dividing by 9, I'm pretty certain the remainder is 4.

3 to the first power is 3, of course. 3 to every power greater than 1 is either 9 or divisible by 9, that leaves you a leftover 1 (8 from 9) and a leftover 3 (the first 3 to the first power).

 

[biglou]

9 is a very interesting number, too. Any factor of nine, its digits can be added to result in nine, or a number divisible by nine, in which case you add those digits together, and repeat as necessary. Examples:

3x9=27. 2+7=9

27x27=729. 7+2+9=18. 1+8=9

etc. it always works. (try it with any factor of nine) I'm pretty sure that's where your pattern lies. which still leads me to believe the answer is 4. Because you will have a remainder of 1 (9-8), plus the first 3 that got added in the very beginning.

Off to google I go! :)

 

[MikeT]

Short answer: it's the cube root of 3, squared. (3 to the .667 power).

I know that I can just use a calculator that can put (in this case) 3 to the .667 power, but if my calculator does not have that y to the x key, how can this problem be done? All the buttons that are available are the square root key and the squared key.

 

[High Lord Gomer]

what is the remainder when 3^0+3^1+3^2...3^2009 is divided by 8?

A) 0
B) 1
C)2
D)4
E)6

It's D) 4

For the sequence:
Power Sum Remainder
0 1 1
1 4 4
2 13 5
3 40 0
4 121 1
5 364 4
6 1093 5
7 3280 0

It cycles through and repeats every 4th power. Since 2008 is divisible by 4 evenly, it will have the same remainder as 0, 4, 8, 12, etc. 2009 would have the next in sequence, or the same as 1, 5, 9, etc. So 2009 would be 4, or D.

 

[FruDaddy]

A little useful reading:
http://www.tpub.com/math1/8c.htm

 

[High Lord Gomer]

A little useful reading:
http://www.tpub.com/math1/8c.htm

Thanks, that made a lot more sense after reading that!

 

[holeshot]

Shoot.........I thought I forgot everything, not the case

Simple stuff

it's 3 squared = 9

then cube root of 9 = 2.08 (the answer)


check it ....

2.08 x 2.08 x 2.08 = 9 (or damn close)

 

[biglou]

As usual, my lack of proper training meant I made this much harder than it needed to be! ;)

 

[RM_guy]

You guys need to get out and ride. This is actually pathetic!!! :p