Unit 7, Lesson 4
Negative Exponents with Powers of 10
Accelerated 7
Practice
Problem 1
Write each expression using a single negative exponent.
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\(\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10}\)
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\(\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10}\)
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\((\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10})^2\)
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\((\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10})^3\)
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\((10 \boldcdot 10 \boldcdot 10)^{\text-2}\)
Problem 2
Write each expression as a single power of 10.
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\(10^{\text-3} \boldcdot 10^{\text-2}\)
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\(10^4 \boldcdot 10^{\text-1}\)
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\(\frac{10^5}{10^7}\)
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\((10^{\text-4})^5\)
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\(10^{\text-3} \boldcdot 10^{\text2}\)
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\(\frac{10^{\text-9}}{10^5}\)
Problem 3
Select all of the following that are equivalent to \(\frac{1}{10,000}\):
\((10,\!000)^{\text-1}\)
\((\text{-}10,\!000)\)
\((100)^{\text-2}\)
\((10)^{\text-4}\)
\((\text{-}10)^2\)
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:
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A dump truck is hauling loads of dirt to a construction site. After 20 loads, there are 70 square feet of dirt.
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I am making a water and salt mixture that has 2 cups of salt for every 6 cups of water.
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A store has a “4 for $10” sale on hats.
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For every 48 apples I pick, my students get 24.
Problem 5
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Explain why triangle \(ABC\) is similar to \(EDC\).
- Find the missing side lengths.