Lesson 5
Negative Exponents with Powers of 10
Let’s see what happens when exponents are negative.
Problem 1
Write with a single exponent: (ex: \(\frac{1}{10} \boldcdot \frac{1}{10} = 10^{\text2}\))
 \(\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10}\)
 \(\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10}\)
 \((\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10})^2\)
 \((\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10})^3\)
 \((10 \boldcdot 10 \boldcdot 10)^{\text2}\)
Problem 2
Write each expression as a single power of 10.
 \(10^{\text3} \boldcdot 10^{\text2}\)
 \(10^4 \boldcdot 10^{\text1}\)
 \(\frac{10^5}{10^7}\)
 \((10^{\text4})^5\)
 \(10^{\text3} \boldcdot 10^{\text2}\)
 \(\frac{10^{\text9}}{10^5}\)
Problem 3
Select all of the following that are equivalent to \(\frac{1}{10,000}\):
\((10,\!000)^{\text1}\)
\((\text{}10,\!000)\)
\((100)^{\text2}\)
\((10)^{\text4}\)
\((\text{}10)^2\)
Problem 4
Match each equation to the situation it describes. Explain what the constant of proportionality means in each equation.
Equations:
 \(y=3x\)
 \(\frac12x=y\)
 \(y=3.5x\)
 \(y=\frac52x\)
Situations:

A dump truck is hauling loads of dirt to a construction site. After 20 loads, there are 70 square feet of dirt.

I am making a water and salt mixture that has 2 cups of salt for every 6 cups of water.

A store has a “4 for $10” sale on hats.

For every 48 cookies I bake, my students get 24.
Problem 5

Explain why triangle \(ABC\) is similar to \(EDC\).
 Find the missing side lengths.