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CLEP General Mathematics: Powers Exponents And Roots

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Dividing by 10
move the decimal point the same number of units to the left
1. Divide the coefficients 2. Subtract the exponents
1
Moving the decimal point to the left

2. A very small number such as 0.000000674 can be written with scientific notation as
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
cube root
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
6.74 x 10^-7

3. = 0.1 - or 1 with the decimal point moved one place to the left.
cube-root key
Scientific notation
10^-1
0

4. When working with scientific notation - you are often required to change the location of the decimal point in the coefficient - but when you move the decimal point - you must
Calculator square-root key
adjust the value of the coefficient
the radical sign with a little 3 that indicates the cube root:
exponent

5. Powers of ten can be added or subtracted only when their exponents
2 x 10^9
Are Equal
base
cubed

6. When working with powers of ten and scientific notation it is often necessary to adjust the position of the decimal point in the coefficient or to change the value of the exponent. When changing one of these terms - it is important that
change both terms in order to keep the value the same.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
radical sign
Subtract the exponent

7. For the 10
base
Moving the decimal point to the left
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
exponent

8. Any number with a negative exponent is equal to
increase the power-of-10 exponent by the same number of units
1 divided by that number with a positive exponent
To multiply powers that have the same base:
base

9. Indicates the number to be multiplied.
proper scientific
0
base
perfect square

10. The decimal part
When the exponent of a power-of-10 expression is a negative integer:
Scientific notation
coefficient
move the decimal point the same number of units to the left

11. When you move the decimal point in the coefficient to the left
proper scientific
increase the power-of-10 exponent by the same number of units
Engineering notation
Scientific notation

12. To subtract powers of ten:
9 (3^2 = 9)
Subtract the exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
exponent

13. When you increase the value of the power-of-10 exponent
Scientific notation
move the decimal point the same number of units to the right
Step 1. Divide the coefficients of the terms
move the decimal point the same number of units to the left

14. 0^5 =
0
increase the power-of-10 exponent by the same number of units
Scientific notation
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

15. The square root of 9 is
must be multiples of 3 or 0
itself
base
3

16. Negative cube roots are okay ... negative square roots are
10^1
change both terms in order to keep the value the same.
Not
base

17. 100 - or 1 with the decimal point moved two places to the right
Scientific notation
Step 1. Divide the coefficients of the terms
10^2
base

18. To divide powers that have the same base:
a fractional decimal
0
radical sign
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

19. To divide powers of 10:
must be multiples of 3 or 0
0
perfect square
Step 1. Divide the coefficients of the terms

20. When moving the decimal point to the right (multiplying by 10)
10^1
rewrite one of the terms so that the exponents are equal
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
decrease the value of the exponent by 1 (dividing by 10)

21. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
proper scientific
cubed
1. Multiply the coefficients 2. Add the exponents

22. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
0
adjust the value of the coefficient
coefficient

23. 1^4 =
increase the power-of-10 exponent by the same number of units
3
itself
1

24. The symbol for the square root of a number is the - a sign placed in front of an expression to denote that a root is to be extracted.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^2
0
radical sign

25. Step 1: Add the exponents Step 2: Use the common base
10^1
To multiply powers that have the same base:
exponent
cube root

26. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
the radical sign with a little 3 that indicates the cube root:
10^1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

27. Don't bother trying to find the square root of a negative number.
The solution exists - but not in the real number system.
itself
1
you have to adjust the value of the exponent in order avoid changing the actual value.

28. Because the exponent for the base-10 must be 0 or a multiple of 3 - the coefficient cannot always be a value between -9 and 9. Instead - the coefficients for engineering notation will be between
move the decimal point the same number of units to the left
Because the exponent for the base-10 must be 0 or a multiple of 3 - the coefficient cannot always be a value between -9 and 9. Instead - the coefficients for engineering notation will be between
5
perfect square

29. Valid powers of 10 for engineering notation are:
0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
perfect square
must be multiples of 3 or 0

30. Scientific notation requires there to be only
itself
one digit to the left of the decimal point
1
exponent

31. Represents 1 preceded by 17 zeros and a decimal point.
change both terms in order to keep the value the same.
10^2
10^-1
10^-18

32. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
base
0
2 x 10^9

33. To find the cube root of any number - simply key in the number (the radicand) and press cube-root key. On most calculators - the cube-root function is a 2nd level function. This means you have to press the 2nd key before pressing the key for the
10^1
cube-root key
0
decrease the power-of-10 exponent by the same number of units

34. When you decrease the value of the power-of-10 exponent
0
move the decimal point the same number of units to the right
1. Multiply the coefficients 2. Add the exponents
change both terms in order to keep the value the same.

35. The square of 3 is
9 (3^2 = 9)
Because the exponent for the base-10 must be 0 or a multiple of 3 - the coefficient cannot always be a value between -9 and 9. Instead - the coefficients for engineering notation will be between
10^-2
3

36. To multiply powers of ten:
cubed
Because the exponent for the base-10 must be 0 or a multiple of 3 - the coefficient cannot always be a value between -9 and 9. Instead - the coefficients for engineering notation will be between
Scientific notation
1. Multiply the coefficients 2. Add the exponents

37. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
cube root
cube-root key
change both terms in order to keep the value the same.

38. Allows you to express very large and very small numbers without using large numbers of digits and decimal places. It's all done with powers of ten.
square root
Engineering notation
Step 1. Divide the coefficients of the terms
Scientific notation

39. A number with an exponent of 3 is often said to be
Calculator square-root key
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
2
cubed

40. Numbers with exponents can be directly multiplied or divided only when they have the
Same base
10^2
adjust the value of the coefficient
When the exponent of a power-of-10 expression is a negative integer:

41. An integer that is found by squaring another integer. You already know how to find the square root of 25 because it is a perfect square: 5 x 5 = 25 - or you could write it as 52 = 25. So 25 is a perfect square - and its square root is 5.
perfect square
exponent
To multiply powers that have the same base:
1. Multiply the coefficients 2. Add the exponents

42. There are no special rules for adding and subtracting numbers that are written with exponents.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
5
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
2 x 10^9

43. The cube root of zero is
must be multiples of 3 or 0
Moving the decimal point to the left
itself
0

44. The cube root of a negative number is also a
Moving the decimal point to the left
1 divided by that number with a positive exponent
negative number
one digit to the left of the decimal point

45. When you change the position of the decimal point in a coefficient value
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
change both terms in order to keep the value the same.
Calculator square-root key
you have to adjust the value of the exponent in order avoid changing the actual value.

46. Indicates the number of times the base is to be multiplied.
exponent
1. Divide the coefficients 2. Subtract the exponents
1
0

47. 5^1 =
1
0
5
same exponent

48. To add powers of ten:
Determine the number of times the original decimal has to be multiplied or divided by 10 in order to show one non-zero digit to the left of the decimal point. Multiply the normalized value by a power of 10 that will restore equality. If you multiplie
Because the exponent for the base-10 must be 0 or a multiple of 3 - the coefficient cannot always be a value between -9 and 9. Instead - the coefficients for engineering notation will be between
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
2 x 10^9

49. Any number with an exponent of 1 is equal to
one digit to the left of the decimal point
base
itself
0

50. A number with an exponent of 2 is often said to be
Not
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
squared
5