Grade 8

End-of-Unit Assessment

End-of-Unit Assessment
Sidekick End-of-Unit Assessment
1.

Which expression is equivalent to 353^5?

A.

31035\dfrac{3^{10}}{3^5}

B.

31533\dfrac{3^{15}}{3^3}

C.

91035\dfrac{9^{10}}{3^5}

D.

9395\dfrac{9^3}{9^5}

2.

Choose the expression that is NOT equivalent to 252^5.

A.

2⋅2⋅2⋅2⋅22 \cdot 2 \cdot 2 \cdot 2 \cdot 2

B.

23⋅2523\dfrac{2^{3} \cdot 2^{5}}{2^{3}}

C.

20⋅252^{0} \cdot 2^{5}

D.

−2−5-2^{-5}

3.

Which expression has a value of 116\dfrac{1}{16}?

A.

(2−4)−1\left(2^{-4}\right)^{-1}

B.

(24)−1\left(2^{4}\right)^{-1}

C.

(28)−2\left(2^{8}\right)^{-2}

D.

(2−8)−2\left(2^{-8}\right)^{-2}

4.

A student claims the expressions 5753\dfrac{5^7}{5^3} and 56×5−25^6 \times 5^{-2} are equivalent. Is the student correct?

Be sure to include what you know about properties of exponents and the value of each expression in simplest form in your answer.

Explain how you determined your answer.

5.

In 2015, there were about 22 million teenagers (aged 13–17) in the United States. They each sent an average of 900 text messages per month. Estimate how many text messages were sent in 2015 by teenagers in the United States in one month. Express your answer using scientific notation.

6.

Here are the approximate populations of three countries, expressed in scientific notation: Panama: 4×1064 \times 10^6; Peru: 3.2×1073.2 \times 10^7; Thailand: 7×1077 \times 10^7.

  1. Lin says that more than 20 times as many people live in Thailand than in Panama. Do you agree with Lin? Explain or show your reasoning.
  2. What is the population of all three countries together?

Answer Key

1.
A
2.
D
3.
B
4.

Yes, the student is correct. 5753=57−3=54\dfrac{5^7}{5^3}=5^{7-3}=5^4 by the quotient rule, and 56×5−2=56+(−2)=545^6\times 5^{-2}=5^{6+(-2)}=5^4 by the product rule. Both simplify to 54=6255^4=625.
5.

An estimate between 1.8×10101.8 \times 10^{10} and 2.2×10102.2 \times 10^{10} is reasonable. Multiply (22×106)⋅(9×102)=198×108=1.98×1010(22 \times 10^6) \cdot (9 \times 10^2) = 198 \times 10^8 = 1.98 \times 10^{10}. Students may also use 20×10620\times10^6 for 22 million, or 1,000 for 900 texts.
6.
  1. No, I do not agree with Lin. Sample reasoning: 20 times Panama's population is 20×(4×106)=8×10720 \times (4\times 10^6) = 8\times 10^7, but Thailand's population is only 7×1077\times 10^7, which is less than 8×1078\times 10^7.
  2. 1.06×1081.06\times 10^8 people (or about 100 million people, or equivalent).