Log inSign up for FREE
Library

CK 9.3 - The Power of 0 and negative exponents

Last updated over 2 years ago
27 questions
0.5

Microscopic Numbers

Biologists and doctors regularly work with cells and other structures that are too small to be seen without the aid of a microscope. One of the ways the health of a cell is determined is by the size. Cells which are abnormally large can be an indicator of a serious illness.

How do you think the size of a cell is measured? (how do biologists TAKE the measurments?)

1

When do you think you would use a microscopic ruler and when do you think you would use relative sizing (sizing compared to other objects/scales/references) ?

The Zero Power

Before you get to the microscopically small, you need to start at zero. If an exponent means to multiply the base that number of times how can something be multiplied zero times? Use the interactive below to explore this idea.

Go to CK12 to use the interactive "zero power" there
1

1

1

1

1

Select all the true statements

What Are Negative Powers?

Continuing the pattern metaphor from the interactive in the previous section, look at this pattern: 2, 4, 8, 16, 32,... the number before 2 in this pattern would be represented by 20 and equal to 1, but what number would come before that? Use the interactive below to explore the idea of negative exponents.

Complete the Interactive on the same page titled "Negative powers"
1

1
Anthing to the -2 power is _______ divided by the base_______ times
Use the interactive below and answer questions to see how patterns in positive exponents relate to negative exponents.
1

1

Notice the values of the exponents in the numerators and denominators.
Note that each of the bases are natural numbers. Select all that apply:

1

There is one answer that stays the same as you change the value of the bases. Based on this observation, one could assume that a number raised to an exponent of 0 is always equal to....

1

What patterns do you observe in the answers on the far right as you move the red point?

1

Many mathematicians argue that 0^0 is undefined. How could they have reached this conclusion?

Simplifying Negative Powers

Since negative exponents represent division, a number to a negative power represents a fraction of 1. Biologists and doctors often write the size of cells and other microscopic organisms using negative exponents. In general, the size of a human cell is about 10−6  meters. This expression simplifies to the following:


Another way to think of this is to find the reciprocal of the fraction with the opposite value for the exponent.

So, Another way to think of 10^ - 6 is as the reciprocal of 10 with an exponent of 6, which would be 1/10^6

Use the interactive from the CK12 page titled "Simplifying negative exponents", then complete the problems below
1
Another way to think of negative exponents is to find the _______ of the fraction with the opposite value for the exponent
1

1

1

1

1

1

1

In general, you never want to write a negative exponent. All exponents should be written as positive.

To convert a negative exponent to a positive exponent, move the base to the other side of the fraction and write the opposite value of the exponent.

1

1

1

1

A positive number raised to a very large negative exponent is less than zero.

1

At a basic level computers perform all of their calculations using powers of two. What kinds of values must a computer use a negative power of two to calculate?