Exercise 18 Page 340

We know that a dinoflagellate is 1000 micrometers long. A microscope magnifies it 100 times. We want to find the length of magnified dinoflagellate in meters. We will start by expressing the length of the organism in meters.

Unit of Length	Length (meter)
Micrometer	10^(- 6)

A micrometer is 10^(- 6) meters. Using this value we can rewrite the length of the dinoflagellate in meters. 1000 micrometers = 1000 * 10^(- 6) metersLet's evaluate the length of the organism in meters! First, we rewrite 1000 as a power 10^3. 1000 * 10^(- 6) meters = 10^3 * 10^(- 6) meters Now, we have a product of powers with the same base. Let's use the Product of Powers Property to simplify this expression.

10^3 * 10^(- 6) meters

MultPow

a^m*a^n=a^(m+n)

10^(3+(- 6)) meters

AddNeg

a+(- b)=a-b

10^(3 - 6) meters

SubTerm

Subtract term

10^(- 3) meters

We found the length of the organism in meters and we know that the microscope magnifies it 100 times. This means we need to multiply the length of the organism by 100 to calculate the magnified length of the dinoflagellate. 100 * 10^(- 3) meters Again, to calculate the product, we will rewrite 100 as a power, and then use the Product of Powers Property.

100 * 10^(- 3) meters

WritePow

Write as a power

10^2 * 10^(- 3) meters

MultPow

a^m*a^n=a^(m+n)

10^(2 + (- 3)) meters

AddNeg

a+(- b)=a-b

10^(2 - 3) meters

SubTerm

Subtract term

10^(- 1) meters

The magnified length of the dinoflagellate is 10^(- 1) meters. Notice that we can rewrite this negative exponent also as 110 meters or 0.1 meters.