Lesson 5: Practice Problems

Problem 1

Write with a single exponent: (ex: $\frac{1}{10} \cdot \frac{1}{10} = 10^{- 2}$ )

$\frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10}$
$\frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10}$
${(\frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10})}^{2}$
${(\frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10})}^{3}$
${(10 \cdot 10 \cdot 10)}^{- 2}$

Problem 2

Write each expression as a single power of 10.

$10^{- 3} \cdot 10^{- 2}$
$10^{4} \cdot 10^{- 1}$
$\frac{10^{5}}{10^{7}}$
${(10^{- 4})}^{5}$
$10^{- 3} \cdot 10^{2}$
$\frac{10^{- 9}}{10^{5}}$

Problem 3

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

${(10, 000)}^{- 1}$
$(- 10, 000)$
${(100)}^{- 2}$
${(10)}^{- 4}$
${(- 10)}^{2}$

Problem 4 From Unit 3 Lesson 2

Match each equation to the situation it describes. Explain what the constant of proportionality means in each equation.

$y = 3 x$
$\frac{1}{2} x = y$
$y = 3.5 x$
$y = \frac{5}{2} x$

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 From Unit 2 Lesson 8

Two triangles ABC and CDE that share a vertex at C. ABC has legs 10 and ?, and hypotenuse 26. Triangle CDE has legs 36, ?, and hypotenuse 39.

Explain why triangle $A B C$ is similar to $E D C$ .
Find the missing side lengths.