Question

Multiply or divide as indicated. Simplify your answer, if possible. (Do not express answer in exponential form.)

Expression below.

Answer 1

\[\frac{ 10 }{ 10^{-2}}\]

I think the answer would be \[10^{-2}\] but the answer has to be 4 numbers long.

Answer 2

the - and the 2 are one thing so the answer 10^-2 is 3 spaces, not 4.

Answer 3

What you have is 10 divided by 10^-2. 10^-2 is actually 1/10^2, or 1/100. So dividing 10 by 1/100 requires some fractional division if your scientific calculator doesn't do that for you:
\[\frac{ 10 }{ 1 } \times \frac{ 100 }{ 1 } = 1000\]
Because with fractional division you multiply by the reciprocal of the second fraction. Make sense?

Answer 4

use the laws of exponents

it equal 10^1 / 10^-2

when you divide as above what do you do with the exponents?

Answer 5

once you have the answer in exponent form convert to normal numbers

Answer 6

@SapphireMoon Yes I understand now.

@welshfella Well in the lesson I'm given if you have something like x^3 / x^-2 I'd end up getting x^1.

Answer 7

x^3 / x^-2 = x^(3-(-2) = x^5

Answer 8

10^1 / 10^-2 = 10^3 = 1000

Answer 9

I was taught to add the exponents not multiply them.

I just looked back at the lesson. That was the rule for the addition and subtraction one. I was using the wrong equation.

Answer 10

you add the exponents when you are multiplying the exponential terms
when dividing the terms you subtract the exponents.

Answer 11

You don't multiply them unless it's something like:
\[(10^{2})^{3} = 10^{6}\]
You add for multiplication of exponents and subtract for division of exponents. So 1 - (-2) = 3 because subtracting a negative number means adding a positive one.

Answer 12

10^4 * 10 ^2 = 10^6

10^4 / 10^2 = 10^(4-2) = 10^2

Answer 13

These are some examples my lesson is giving me. The thing is if I put this it wont be enough to actually fill in the amount of letters I need for the full answer.

Answer 14

It does look like I have to add though.

Answer 15

Manipulating exponential terms comes easy with practice.
You just need to know the 3 main rules.

Answer 16

where do you think you have to add?
In the question you posted?

Answer 17

Looking back at the lesson, it looks like I have to subtract instead of add since the numerators exponent is positive and the denominators is negative.

Answer 18

Since it's a division problem. If it were a multiplication problem I'd add.

Answer 19

Yes
When its a multiplication problem you add exponents
division - you subtract exponents.

Answer 20

the fact that the numerator is positive and denominator is a negative has nothing to do with the choice.

Answer 21

^^

Answer 22

Okay, I know that now.

So the answer would be 1,000 like @SapphireMoon said since I'm solving it.

Answer 23

Yep!

Answer 24

yes
I think they want you to use exponent processing first then convert to normal form later.
But converting to normal form first then simplifying gives the same answer.

Answer 25

- but i may be wrong. Ill think you'll get the same credit whichever way.

Answer 26

Thanks to both of you for all of your help.

Answer 27

You're welcome! I remember struggling with this in prealgebra (or whenever it was, a very long way from precal anyways), happy to help!

Answer 28

yw

Answer 29

If few more facts about exponents
x can be written as x^1 6 = 6^1 abd so on.
x^0 ( in fact any variable or number with exponent 0) = 1

Answer 30

y^0 = 1 , 1563^0 = 1 etc