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6-8 Accelerated 7 Unit 7 Lesson 4

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IM K-5 Math
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Unit 7, Lesson 4

Negative Exponents with Powers of 10

Accelerated 7

Practice

Problem 1

Write each expression using a single negative exponent.

\(\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10}\)
\(\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10}\)
\((\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10})^2\)
\((\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10})^3\)
\((10 \boldcdot 10 \boldcdot 10)^{\text-2}\)

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Problem 2

Lesson 4 Resources

Student Materials

Write each expression as a single power of 10.

\(10^{\text-3} \boldcdot 10^{\text-2}\)
\(10^4 \boldcdot 10^{\text-1}\)
\(\frac{10^5}{10^7}\)
\((10^{\text-4})^5\)
\(10^{\text-3} \boldcdot 10^{\text2}\)
\(\frac{10^{\text-9}}{10^5}\)

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Problem 3

Select all of the following that are equivalent to \(\frac{1}{10,000}\):

\((10,\!000)^{\text-1}\)
\((\text{-}10,\!000)\)
\((100)^{\text-2}\)
\((10)^{\text-4}\)
\((\text{-}10)^2\)

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Problem 4

ForLesson 2: Representing Proportional Relationships

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 apples I pick, my students get 24.

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Problem 5

ForLesson 13: Similar Triangles

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

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