true or false A number with a negative exponent does not have a reciprocal

Answer 1

two numbers are reciprocals of each other if their product is 1

(2/3)(3/2)=6/6=1

2^-3 has a reciprocal

2^-3=1/2³=1/8

the reciprocal is 8/1 or 8

another way to look at it is the following...

2^-3 times what number gives you 1 ?

2⁰=1

therefore, -3 plus what number is 0? the answer is 3

the reciprocal of 2^-3 is 2³ because when you multiply the numbers you get 2^(-3+3)=2⁰=1

2^-3=1/8 and 2³=8 and (1/8)(8)=1

Answer 2

This is a false statement. it IS possible for a number with a negative exponent to have a reciprocal.

Remember a reciprocal is one divided by a number (like an inverse of a fraction).

For example, the reciprocal of 2/3 is 3/2. Also the reciprocal of 4 is 1/4.

A negative exponent means that you perform the exponent on the reciprocal of the number.

For example, 2^-2 is simplified to 1/2² = 1/4

However, that final number can still have its own reciprocal. You just flip the fraction like we did before.

1/4 -> 4/1

So the reciprocal of 2^-2 (which equals 1/4) is 4. This is a totally possible and real solution.

Here is an example using x if that makes more sense for you.

Let's say x is your original number. With a negative exponent it may look like this: x^-2

If you were to simplify this, you would get (1/x²)

The reciprocal of THAT fraction is x²

SO the reciprocal of x^-2 is x².

Let me know if I can explain this further!