Real Numbers, Exponents, Scientific
Notation and Roots Review
9
1. Write − 15 as a decimal.
Name: _______________________
Date: _______ Color: ________
̅̅̅ as a fraction in
2. Write 0. ̅75
simplest form.
Simplify the expression. The simplified expression should have no negative
exponents.
3. 43 × 45
4. (23 )4
5. (−6𝑎)3
6. (4𝑥𝑦 2 )2
7. 5(5−3 )
8. (3)−3
9.
(−3𝑥 2 𝑦)−2
(2−2 𝑥𝑦 −3 )2
11. 𝑥 3 𝑦 −5
2
10.
12.
6𝑥 4 𝑦 3
5𝑥𝑦 2
25𝑥 5 𝑦 3
∗ −3𝑥 3 𝑦 7
4
3𝑥 −5 𝑦 −6
Rewrite the number in standard form.
13. 6.15 x 105
14. 1.4 x 10-6
Rewrite the number in scientific notation.
15. 0.000647
16. 54,900,000
Solve. Write your answer in scientific notation.
4.5 × 10−3
17. (3.1 x 10-2) x (9.6 x 106)
18.
19. (5.62 x 105) – (5.3 x 105)
20. (6.4 x 104) + (5.92 x 106)
5 × 10−5
21. Recently in the United States, there were 300,000,000 cell phone users. That
same year, there were 5.7 x 109 cell phone users worldwide. About how many times
larger was the number of cell phone users worldwide than in the United States?
22. In 2010, the population of a city was 100,000. Then each year for the next
five years, the population increased by 3%. Write the exponential model that
represents this situation.
23. You buy a used truck for $12,000. It depreciates at the rate of 18% per year.
Write the exponential model that represents this situation.
Classify the model as exponential growth or exponential decay. Identify the
growth or decay factor and the percent of increase or decrease per time period.
24. 𝑦 = 17(1.9)𝑥
25. 𝑦 = 22(0.8)𝑥
26. 21. What is the value of the expression
144
−√100
22. To the nearest whole number,
what is the best estimate of √214
23. The area of a square sandbox is 83 square feet.
To the nearest foot, what is the perimeter of
the sandbox?
24. What is the value of √216?
3
30. Estimate √130 to the nearest whole number.
3
25. Solve the equation 𝑥 2 = 400.