Name:___________________________ Date:______________
Unit 2 Study Guide
1. x² • x 4 • x³ = _____𝑥 9 __ The base is the same, you are multiplying add the exponents.
2. 4m 4 (n 7 m) = ______4𝑚5 𝑛7 _____ remove the parentheses and combine the like terms
3.
212
27
= _______25 ________ Base is the same, you are dividing, subtract the exponents
4. (4ab) (5a²b³) =__ 20𝑎3 𝑏 4 ____Multiply the coefficients, add the exponents
5. (4x²y)² (3x²y)= ____48𝑥 6 𝑦 3 ______ Distribute the exponent 2 into each term first;
then, multiply the coefficients, and add the exponents
6. 14a³b 4 =____7𝑎2 𝑏 3 ______ Divide the 14 evenly by 2 (this is coefficient), subtract
2ab
the exponents
7. (5a)² = _____25𝑎2 ______ Distribute the exponent into each term. Simplify 5²
8. y 5 • y² = _____𝑦 7 ______ add the exponents
1
9. 5 2 = _____52 ________ Negative exponents, you must rewrite as fraction with one as
your numerator with the 5² as your denominator. It is no longer negative. It is positive.
10. 12º = _____1_______ anything raised to the 0 power is 1
11. 6³ = ___________ Base is the same, you are dividing, subtract the exponents
6²
Express each number in scientific notation. Large number has a positive exponent. Small
number has a negative exponent. Your answer must be written times a power of 10.
12. 2100 = ___2.1 x 10³___
13. 810.4 =____8.104 x 10²_____
14. 9,750,000 = ____9.75 x 106 ____ 15. .00095 = ____9.5 x 10−4 ________
Express each number in standard form. Positive exponents will be a large number.
Negative exponents will be a small number.
16. 4.2 x 10 4 = ______42,000_____
18. 4.18 x 10 4 = ______41,800_____
17. 5.7 x 10 2 =____.057_______
Find the product. Write the answer in scientific notation. Multiply the coefficients and
subtract the exponents. Make sure your answer is in scientific notation (the coefficient
must be between 1-10)
19. (2.5 x 10 4 ) (3 x 10²) = __7.5 x 106 ___ 20. (5 x 10 3 ) (7 x 10 8 ) = __3.5 x 106 __
21. (6.9 x 107 ) (9 x 105 ) = __6.21 x 1013 ___ 6.9 x 9 will give you 62.1. This is not in
scientific notation. You must move the decimal one time to the left and add one point to
the exponent.
Find the quotient. Write your answer in scientific notation. Divide the coefficients and
subtract the exponents. Make sure your answer is in scientific notation (the coefficient
must be between 1-10)
22. (3.72 x109 ) ÷ (1.2 x105 ) = ____3.1x 104 _____
23. (6.4 x10−4) ÷ (4 x106 ) = ______1.6 x _10−10 ___
24. (1.23 x1011 ) ÷ (2.4 x104 ) = ____5.125 x __106 ________ When you divide 1.23 by
2.4, you will get .5125. This is not in scientific notation. You must move the decimal one
time to the right and subtract one from the exponent.
Solve the addition and subtraction problems below. The exponent must be the same. If
you add to the add exponent, you must move the decimal that many places to the left.
25. (1.26 x104 ) + (1.12 x103 ) = _______1.372 x 104 _____
26. (7.49 x105 ) + (6.51 x104 ) = ______8.141 x _105 _____
27. (2.54 x108 ) + (1.52 x107 ) = ______2.692 x __108 _____
28. (5.55 x104 ) – (3.41 x103 ) = _____5.209 x _104 __ ___
29. (1.6 x109 ) – (5.62 x106 ) = _______1.59 x __109 ____
30. (2.22 x103 ) – (1.11 x102 ) = ______2.109 x 103 _____
Find the square and cube root of each number. You must memorize them or learn how to
get them. If it is a perfect square, we multiply a number times itself twice. If it is a perfect
cube, we multiply a number times itself three times to get it.
3
31. √216 = ________6____
32. √81 = ______9_____
34. √36 = _______6________
35. √144 = ____12_______
3
33. √512 = ___8___
Estimate Locate what two prefect squares the number lie between. Determine which one
it is closet too. It is estimated to be that number.
36. √75 ≈ _____9_____
37. √23 ≈ ____5_____
38. √54 ≈ ___7_