# Index form with a prime number base?

• Jul 20th 2010, 04:31 AM
Trillian
Index form with a prime number base?
Hi, I desperately need help in knowing how to solve a problem that requires a number to be written in index form with a prime number base. I can see the answers in the back of the text, but I have no idea how they get those answers. This is for both whole numbers and fractions.

An example of the questions are;

1. 81
2. 1/13
• Jul 20th 2010, 05:19 AM
CaptainBlack
Quote:

Originally Posted by Trillian
Hi, I desperately need help in knowing how to solve a problem that requires a number to be written in index form with a prime number base. I can see the answers in the back of the text, but I have no idea how they get those answers. This is for both whole numbers and fractions.

An example of the questions are;

1. 81
2. 1/13

No, I think you will have to provide more context than that (form what you have posted I have no idea what your question is about)

$81=3^4$, $1/13=13^{-1}$

CB
• Jul 20th 2010, 03:53 PM
Trillian
Sorry, I didn't have much more to include. This is how it appeared in our textbook;

2 Write each number in index form with a prime number base
a) 8
b) 64
c) 81
d) 32
e) 625

3 Write each number in index form with a prime number base
a) 1/13
b) 1/49
c) 1/13^3
d) 1/1024
e) 9/729

There was nothing else to show how you are meant to work it out or anything. There were examples given at the start of the chapter, but they gave the question and then they answered it in the solution, but they didn't demonstrate the method for working it out. A extensive google search showed factor trees, but again there was nothing showing how to apply a method to work out which numbers you needed because for larger numbers there are several prime numbers that could be used if that makes sense.
• Jul 20th 2010, 04:07 PM
eumyang
I personally don't use any method per se in doing these. Maybe for me, I've worked with numbers long enough and I have a good enough memory to figure these out in my head.

For instance (I'll show parts a and e of each)...

2a) $8 = 2 \cdot 2 \cdot 2 = 2^3$
2e) $625 = 5 \cdot 5 \cdot 5 \cdot 5 = 5^4$
3a) $\frac{1}{13} = 13^{-1}$
3e) $\frac{9}{729} = \frac{1}{81} = \frac{1}{3 \cdot 3 \cdot 3 \cdot 3} = \frac{1}{3^4} = 3^{-4}$

Otherwise, factor trees may work. Here's an example showing that 625 = 5 x 5 x 5 x 5:
Attachment 18258
• Jul 20th 2010, 04:17 PM
Trillian
Thank you very much for that. that makes it a bit easier to understand.