Question

Did i do this right?
Simplify each expression. Use Positive exponents
m3 n^-6 p^0.

1n^-6/1 = 1/n^-6 now we put the positive n^6 back in it's original place.

m^3 n^6 p

Answer 1

uhhhh i think so i belive so

Answer 2

The rule for negative exponents is:

\(\Large\color{black}{ \displaystyle \color{blue}{\rm a}^{-\color{red}{\rm b}}=\frac{1 }{\color{blue}{\rm a}^{\color{red}{\rm b}}} }\)

Answer 3

so, your expression is:
\(m^3n^{-6}p^0\)

is that correct?

Answer 4

i may be wrong my b

Answer 5

Okay 1n^-6/1 = 1/n^-6 = 1/n^6 now we put the positive n^6 back in it's original place.

m^3 n^6 p How about now

Answer 6

you are still doing 2 parts incorrectly, not just the n^(-6), but p^0 is incorrect as well-:(

Answer 7

lets start from \(p^0\), ok?

Answer 8

Okay.

Answer 9

The rule for an exponent of 0 is:

\(\Large\color{black}{ \displaystyle \color{blue}{\rm x}^{\color{red}{\rm 0}}=1 }\)

This is true for any value of x, but provided that x is NOT zero.
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ADDITIONALLY:
The prove for this rule is:

\(\Large\color{black}{ \displaystyle \color{blue}{\rm x}^{\color{red}{\rm 0}}=\color{blue}{\rm x}^{w-w} }\)
(i am using w, but you can replace w with 1, 3, or any other number and the statement will still hold)

\(\Large\color{black}{ \displaystyle \color{blue}{\rm x}^{\color{red}{\rm 0}}=\color{blue}{\rm x}^{w-w} =\dfrac{x^w}{x^w}=1}\)

(anything divided by itself gives a result of 1, but if x was 0 then we have 0/0 which is not defined. This is why I said every x but NOT x=0)

Answer 10

So if any number (except 0) raised to the power of 0, gives a result of 1, then
\(p^0={\rm what?}\)

Answer 11

((Another NOTE: they didn't state that \(p\ne0\), it is their fault, but you have to make this assumption, to get the answer, or else it would be indeterminate))

Answer 12

Alright.

Answer 13

So p^1?

Answer 14

p^1 ? you don't have that in your expression, do you?

Answer 15

No, so do i leave the p^0 alone?

Answer 16

you have p^0, and you know that:

(anything)\(^0\) = ?

Answer 17

x?

Answer 18

(anything)\(^0\)=1
(as long as this anything is NOT zero)

Answer 19

therefore, you can say that

p\(^0\)=?

Answer 20

But p has a zer exponent?

Answer 21

yes, so p\(^0\)= what?

Answer 22

Zero* And is it 1

Answer 23

yes, p\(^0\)=1

Answer 24

So lets re-write our expression

\({\rm m}^3\cdot {\rm n}^{-6} \cdot {\rm p}^0\)

this kis what it is used to be, but we know p\(^0\)=1, so we can say:

\({\rm m}^3\cdot {\rm n}^{-6} \cdot 1\)

and multiplying times 1, is not changing the value, so we can leave the "•1" part out. (right?)

We have: \({\rm m}^3\cdot {\rm n}^{-6} \)

Answer 25

is everything making sense till this point?

Answer 26

Alright. Yeah so far.

Answer 27

Because the p is = to 1 right?

Answer 28

yes, because p\(^0\)=1

Answer 29

So yeah i get it not sure why we need to leave the 1 out after solving the problem though.
Is it because it's exponent was 0?

Answer 30

why we have to leave the "•1" out?
Not that we must, but it does matter.

For any number, if you multiply it times 1 you still have that same number.
Multiplying times 1 is same, and just as good as, not multiplying by anything at all.

Answer 31

Makes sense. Thanks for your help.

Answer 32

we aren't done yet.

Answer 33

Alright

Answer 34

So our new expression is:
\({\rm m}^3\cdot {\rm n}^{-6} \)

And, this can be simplified more.
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Now, if we can recall, I mentioned another important property, and it refers to negative exponents. This property is:

\(\Large\color{black}{ \displaystyle \color{blue}{\rm a}^{-\color{red}{\rm b}}=\frac{1 }{\color{blue}{\rm a}^{\color{red}{\rm b}}} }\)

Answer 35

according to this property,

\(\Large\color{black}{ \displaystyle \color{blue}{\rm n}^{-\color{red}{\rm 6}}=\frac{1 }{\color{blue}{\rm n}^{\color{red}{\rm 6}}} }\)

right?

Answer 36

Yeah

Answer 37

same, but n instead of a, and 6 instead of b.

good...

Answer 38

n^-6/1/n^6

Answer 39

n\(^{-6}\) = 1 / n\(^6\)

like this, you mean?

Answer 40

Yeah forgot to put in my equal.

Answer 41

lol.

Answer 42

:P

Answer 43

so, we had:

\({\rm m}^3\cdot {\rm n}^{-6} \)

and now we know that: \( {\rm n}^{-6}=\dfrac{1}{{\rm n}^6} \)
So, we can re-write our expression the following way:

\({\rm m}^3\cdot\dfrac{1}{{\rm n}^{6}} \)

Answer 44

then you can make it as 1 fraction, just the following way:

\({\rm m}^3\cdot\dfrac{1}{{\rm n}^{6}} \)


\(\dfrac{{\rm m}^3}{1}\cdot\dfrac{1}{{\rm n}^{6}} \)


\(\dfrac{{\rm m}^3\cdot 1}{1\cdot {\rm n}^{6}} \)


\(\dfrac{{\rm m}^3}{{\rm n}^{6}} \)

Answer 45

if you have any questions regarding any of the rules or steps that were aplied or mentioned, please ask...

Answer 46

No questions, because you timing it by one which would make it the same number.

Answer 47

alright.
G☼☼d luck

Answer 48

Thanks :)