How do you simplify the following expressions?

1. Mar 21, 2012

hexhall

I'm only in 9th grade math, so please don't give me complicated calculus answers. And I prefer if you give steps on how to solve each step. Thanks in advance!

1. 5^-2/p
2. 3x^-2/y
3. (x^-5) (y^-7)
4. 8/2c^-3
5. (6a^-1) (c^-3)/d^0
6. (9^0) (y^7) (t^-11)

2. Mar 21, 2012

PeterO

Unusual that you post this on the Physics forum but ...

Simplifying in indice problems usually means either

collecting all terms in the numerator
or
expressing without negative indices,
and
perhaps evaluating numerical indices

I that order, number 1 becomes:

5-2p-1
or
1/(52p)
or
1/(25p)

really depends which one of those you think is the most simplified.

Note: I typed in brackets in the 2nd and 3rd example lest you thought only the first part was in the denominator.
When writing by hand you can make a clear fraction with a large dividing line so it is clear both the 25 and p, for example, are in the denominator.

With indices, combining those indices with the same base usually constitutes simplification, but that does not apply to any of these examples.

3. Mar 21, 2012

hexhall

I still don't really understand the process in which you figured it out...

4. Mar 21, 2012

PeterO

Does that mean you don't understand negative indices?

That is a more basic problem if that is the case.

5. Mar 21, 2012

hexhall

Yes... Could you just explain it one more time, please?

6. Mar 21, 2012

PeterO

2-3 = 1/23

going out now won't have a further reply for 8 hours.

7. Mar 21, 2012

hexhall

Okay, well, that didn't really answer my question...? Is this a new problem? I don't think you get what I'm asking.

8. Mar 21, 2012

emailanmol

Hey,

See x^3 is like saying x*x*x.

On the other hand x^(-3) is like saying (1/x)*(1/x)*(1/x)

That is (1/x^3).

So 5^(-2)/p is like (1/5)*(1/5)*(1/p) so its (1/25p)

Is it clear??

In general x^a is like multiplying x with itself a times.

x^(-a) is like multiplying
(1/x) a times.

9. Mar 21, 2012

emailanmol

10. Mar 22, 2012

PeterO

Not really sure even YOU know what you are asking.

In post#2 I gave you the 3 most likely answer to the first problem. Which one is "correct" depends on the context in which the questions were given.

As I said:

Some people think expressing indices with a denominator of 1 is it.

Some people think using only positive indices is it.

Some people think that evaluating every indice that has a number as a base is what is required.

What do you think is required?

11. Mar 22, 2012

hexhall

Hey, you answered one of my other questions! Thanks for explaining it into simpler terms. And thanks for the links too. I get it now