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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. To multiply powers of 10:
same exponent
exponent
1
Step 1. Multiply the coefficients of the factors. The result is the coefficient of the product. Step 2. Add the exponents of the factors. The result is the exponent of the product. Of course the base of 10 remains unchanged.

2. Indicates the number of times the base is to be multiplied.
10^-18
exponent
base
Moving the decimal point to the left

3. A number with an exponent of 2 is often said to be
10^-18
squared
perfect square
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

4. Is a special form of power-of-10 notation where the exponents for the 10s must be 0 or multiples of 3. There must be 1 - 2 - or 3 digits on the left side of the decimal point.
Engineering notation
Are Equal
1
cubed

5. Scientific notation requires there to be only
cube root
Same base
one digit to the left of the decimal point
2

6. To add or subtract numbers written with exponents:
exponent
adjust the value of the coefficient
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
proper scientific

7. Any number with a negative exponent is equal to
1
1 divided by that number with a positive exponent
decrease the power-of-10 exponent by the same number of units
rewrite one of the terms so that the exponents are equal

8. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
move the decimal point the same number of units to the right
9 (3^2 = 9)
10^-2

9. 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
0
1
0

10. A number with an exponent of 3 is often said to be
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
change both terms in order to keep the value the same.
the radical sign with a little 3 that indicates the cube root:

11. Valid powers-of-10 for engineering notation
increase the power-of-10 exponent by the same number of units
Are Equal
0
must be multiples of 3 or 0

12. The cube root of zero is
6.74 x 10^-7
Step 1. Multiply the coefficients of the factors. The result is the coefficient of the product. Step 2. Add the exponents of the factors. The result is the exponent of the product. Of course the base of 10 remains unchanged.
same exponent
0

13. 1 to any power is equal to
2
1
0
9 (3^2 = 9)

14. Multiplying by 10
2 x 10^9
Moving the decimal point to the right
1
Because 4 multiplied by itself equals 16.

15. When you decrease the value of the power-of-10 exponent
0
move the decimal point the same number of units to the right
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
a fractional decimal

16. Valid powers of 10 for engineering notation are:
6.74 x 10^-7
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
change both terms in order to keep the value the same.
base

17. When you move the decimal point in the coefficient to the right
decrease the power-of-10 exponent by the same number of units
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-18
must be multiples of 3 or 0

18. 5^1 =
negative number
6.74 x 10^-7
Scientific notation
5

19. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
1 divided by that number with a positive exponent
2 x 10^9
base
same exponent

20. To subtract powers of ten:
Step 1. Divide the coefficients of the terms
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0
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

21. 0 to any power is equal to
0
the radical sign with a little 3 that indicates the cube root:
radical sign
decrease the value of the exponent by 1 (dividing by 10)

22. The square root of 9 is
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
squared
3
5

23. Represents 1 preceded by 17 zeros and a decimal point.
10^1
1
one digit to the left of the decimal point
10^-18

24. The square of 3 is
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Engineering notation
9 (3^2 = 9)
1. Divide the coefficients 2. Subtract the exponents

25. Numbers with exponents can be directly multiplied or divided only when they have the
Same base
When moving the decimal point to the left (dividing by 10)
exponent
0

26. 100 - or 1 with the decimal point moved two places to the right
10^2
move the decimal point the same number of units to the left
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1. Multiply the coefficients 2. Add the exponents

27. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
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
adjust the value of the coefficient
1 divided by that number with a positive exponent
Subtract the exponent

28. The cube root of a negative number is also a
1
Step 1. Divide the coefficients of the terms
negative number
Are Equal

29. Dividing by 10
Moving the decimal point to the left
squared
9 (3^2 = 9)
1

30. Powers of ten can be added or subtracted only when their exponents
10^-2
Are Equal
cube-root key
Moving the decimal point to the right

31. Always 10 for scientific notation
1
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
base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

32. 10 - or 1 with the decimal point moved one place to the right
exponent
10^1
must be multiples of 3 or 0
Because 4 multiplied by itself equals 16.

33. 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.
square root
radical sign
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1. Divide the coefficients 2. Subtract the exponents

34. Any number with an exponent of 0 is equal to
1
a fractional decimal
Step 1. Divide the coefficients of the terms
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

35. To add powers of ten:
increase the power-of-10 exponent by the same number of units
base
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
you have to adjust the value of the exponent in order avoid changing the actual value.

36. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
0
2 x 10^9
exponent

37. 3^0 =
exponent
1
0
proper scientific

38. For the 10
exponent
adjust the value of the coefficient
9 (3^2 = 9)
cube root

39. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
Calculator square-root key
1 divided by that number with a positive exponent
a fractional decimal

40. 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
When moving the decimal point to the left (dividing by 10)
Moving the decimal point to the right
change both terms in order to keep the value the same.
base

41. Negative cube roots are okay ... negative square roots are
Not
negative number
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 4 multiplied by itself equals 16.

42. Any number with an exponent of 1 is equal to
Subtract the exponent
perfect square
10^1
itself

43. The square root of zero is
rewrite one of the terms so that the exponents are equal
0
Subtract the exponent
Step 1. Divide the coefficients of the terms

44. = 0.01 - or 1 with the decimal point moved two places to the left.
cubed
perfect square
0
10^-2

45. 10^-1 = 0.1 - or 1 with the decimal point moved one place to the left. 10^-2 = 0.01 - or 1 with the decimal point moved two places to the left. 10^-18 represents 1 preceded by 17 zeros and a decimal point.
When the exponent of a power-of-10 expression is a negative integer:
one digit to the left of the decimal point
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1 divided by that number with a positive exponent

46. 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
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
proper scientific
Step 1. Multiply the coefficients of the factors. The result is the coefficient of the product. Step 2. Add the exponents of the factors. The result is the exponent of the product. Of course the base of 10 remains unchanged.
cube-root key

47. 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
adjust the value of the coefficient
When the exponent of a power-of-10 expression is a negative integer:
3
Are Equal

48. To divide powers of 10:
Are Equal
move the decimal point the same number of units to the left
Step 1. Divide the coefficients of the terms
proper scientific

49. To divide powers of ten:
perfect square
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
1
1. Divide the coefficients 2. Subtract the exponents

50. To divide powers that have the same base:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
9 (3^2 = 9)
Engineering notation