Please answer, negative exponent.

[Kaseydog]

I'm a parent having a difference of opinion with a teacher. What is the reciprocal of 10^-3?

This is how I worked it out:

According the rules of negative exponents, 10^-3 =1/10³ .

1/10³ = 1/1000

The reciprocal of which is 1000, or 10³ .

Therefore, the reciprocal of 10^-3 is 10³ , correct?

 

[stapel]

I'm a parent having a difference of opinion with a teacher. What is the reciprocal of 10^-3?

This is how I worked it out:

According the rules of negative exponents, 10^-3 =1/10³ .

1/10³ = 1/1000

The reciprocal of which is 1000, or 10³ .

Therefore, the reciprocal of 10^-3 is 10³ , correct?

What is your answer? What is the teacher's answer? Thank you!

 

[pka]

I'm a parent having a difference of opinion with a teacher. What is the reciprocal of 10^-3?
This is how I worked it out:
According the rules of negative exponents, 10^-3 =1/10³ .
1/10³ = 1/1000
The reciprocal of which is 1000, or 10³ .
Therefore, the reciprocal of 10^-3 is 10³ , correct?

The term reciprocal means multiplicative inverse.
What times \(\displaystyle 10^{-3}\) gives \(\displaystyle 1~?\) Well it is \(\displaystyle 10^{3}\).
So \(\displaystyle 10^{3}\) is the answer.

 

[Kaseydog]

What is your answer? What is the teacher's answer? Thank you!

The teacher is saying that it is 1/10^{3 .}

 

[Kaseydog]

The term reciprocal means multiplicative inverse.
What times \(\displaystyle 10^{-3}\) gives \(\displaystyle 1~?\) Well it is \(\displaystyle 10^{3}\).
So \(\displaystyle 10^{3}\) is the answer.

Thank you. I don't want to start WWlll with this lady, but I know it's not right.

 

[stapel]

What is your answer? What is the teacher's answer?

The teacher is saying that it is 1/10³

That's wrong: 1/10³ is equal to 10^-3; it's certainly not the reciprocal of it! Maybe the teacher meant tosay that 1/10^-3 was the reciprocal...?

 

[pka]

Thank you. I don't want to start WWlll with this lady, but I know it's not right.

If I were you, I would politely ask her to look at this thread.

 

[mathprogram]

Correct answer

You're correct. The reciprocal of an exponent is the -1 * the exponent. So in the case of 10^-3, the reciprocal is 10³

 

[Steven G]

I'm a parent having a difference of opinion with a teacher. What is the reciprocal of 10^-3?

This is how I worked it out:

According the rules of negative exponents, 10^-3 =1/10³ .

1/10³ = 1/1000

The reciprocal of which is 1000, or 10³ .

Therefore, the reciprocal of 10^-3 is 10³ , correct?

You are correct and the teacher is wrong. Math teachers do not usually have a good command of the language they teach. They say take the reciprocal but they really are not doing that.

(anything) raised to the -1 power is the reciprocal of the (anything).

Now 1/10^(-3) =(1/10)^(-3)= [(1/10)^(-1)]^(3)= [10]^3=1000