# How do you simplify the following expressions?

• hexhall
In summary, the conversation is about simplifying expressions with negative indices. The person asking the question is in 9th grade and prefers if the steps for solving each problem are provided. Through the conversation, the concept of negative indices is explained using examples and helpful links are provided for further understanding. The conversation ends with the person understanding the concept and thanking the other person for their explanation.
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)

hexhall said:
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)

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.

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

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

Does that mean you don't understand negative indices?

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

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

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

2-3 = 1/23

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

PeterO said:
2-3 = 1/23

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

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

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.

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

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?

emailanmol said:
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.

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

## 1. What does it mean to simplify an expression?

Simplifying an expression means to rewrite it in a simpler form, usually by combining like terms or using mathematical properties to eliminate unnecessary parts of the expression.

## 2. How do you simplify an expression with parentheses?

To simplify an expression with parentheses, you can use the distributive property to remove the parentheses. Multiply the term outside the parentheses by each term inside the parentheses, then combine like terms.

## 3. Can you simplify expressions with exponents?

Yes, expressions with exponents can be simplified using the rules of exponents. For example, when multiplying two terms with the same base, you can add their exponents. When dividing two terms with the same base, you can subtract their exponents.

## 4. What is the difference between simplifying and solving an expression?

Simplifying an expression involves rewriting it in a simpler form, while solving an expression involves finding the value of the expression for a given set of variables or conditions.

## 5. How do you know when an expression is simplified?

An expression is considered simplified when all like terms have been combined and there are no more parentheses or exponents. It should also be in its most compact form, with no unnecessary terms or factors.

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