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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Always 10 for scientific notation
base
exponent
Are Equal
1

2. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
2
decrease the power-of-10 exponent by the same number of units
increase the power-of-10 exponent by the same number of units

3. When moving the decimal point to the right (multiplying by 10)
move the decimal point the same number of units to the right
The solution exists - but not in the real number system.
Not
decrease the value of the exponent by 1 (dividing by 10)

4. 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.
adjust the value of the coefficient
rewrite one of the terms so that the exponents are equal
10^-2
When the exponent of a power-of-10 expression is a negative integer:

5. 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.
10^1
increase the power-of-10 exponent by the same number of units
1. Divide the coefficients 2. Subtract the exponents
radical sign

6. The square root of zero is
1
rewrite one of the terms so that the exponents are equal
10^1
0

7. 0^5 =
a fractional decimal
0
square root
10^-1

8. 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.
Step 1. Divide the coefficients of the terms
1
perfect square
move the decimal point the same number of units to the right

9. 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.
Not
1
0

10. Negative cube roots are okay ... negative square roots are
proper scientific
Not
negative number
1. Divide the coefficients 2. Subtract the exponents

11. A number - when multiplied by itself - is equal to a given number.
square root
10^1
negative number
To multiply powers that have the same base:

12. A number with an exponent of 3 is often said to be
Scientific notation
radical sign
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.
cubed

13. 1^4 =
1
0
0
Subtract the exponent

14. To divide powers of ten:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Because 4 multiplied by itself equals 16.
1. Divide the coefficients 2. Subtract the exponents
same exponent

15. Any number with an exponent of 1 is equal to
cubed
itself
When the exponent of a power-of-10 expression is a negative integer:
10^-1

16. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
10^-18
change both terms in order to keep the value the same.
0

17. Indicates the number to be multiplied.
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.
one digit to the left of the decimal point
base
negative number

18. Dividing by 10
To multiply powers that have the same base:
the radical sign with a little 3 that indicates the cube root:
Moving the decimal point to the left
radical sign

19. To add or subtract numbers written with exponents:
Engineering notation
decrease the value of the exponent by 1 (dividing by 10)
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

20. To divide powers of 10:
Step 1. Divide the coefficients of the terms
1
base
cube-root key

21. Don't bother trying to find the square root of a negative number.
the radical sign with a little 3 that indicates the cube root:
you have to adjust the value of the exponent in order avoid changing the actual value.
The solution exists - but not in the real number system.
0

22. For the 10
exponent
9 (3^2 = 9)
Scientific notation
base

23. The cube root of a negative number is also a
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
negative number
5
adjust the value of the coefficient

24. When you increase the value of the power-of-10 exponent
1
same exponent
move the decimal point the same number of units to the left
cubed

25. 100 - or 1 with the decimal point moved two places to the right
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
negative number

26. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
decrease the value of the exponent by 1 (dividing by 10)
perfect square
one digit to the left of the decimal point
proper scientific

27. 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
Engineering notation
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

28. When you decrease the value of the power-of-10 exponent
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
10^-18
move the decimal point the same number of units to the right

29. A very small number such as 0.000000674 can be written with scientific notation as
To multiply powers that have the same base:
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
6.74 x 10^-7

30. = 0.1 - or 1 with the decimal point moved one place to the left.
1 divided by that number with a positive exponent
coefficient
10^-1
Same base

31. 0 to any power is equal to
move the decimal point the same number of units to the right
10^-1
0
base

32. Numbers with exponents can be directly multiplied or divided only when they have the
the radical sign with a little 3 that indicates the cube root:
The solution exists - but not in the real number system.
Same base
cube-root key

33. The square root of 9 is
increase the power-of-10 exponent by the same number of units
1 divided by that number with a positive exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
3

34. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
exponent
2
one digit to the left of the decimal point
Step 1. Divide the coefficients of the terms

35. When you move the decimal point in the coefficient to the left
2
Engineering notation
increase the power-of-10 exponent by the same number of units
2 x 10^9

36. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
cube-root key
2 x 10^9
decrease the power-of-10 exponent by the same number of units

37. 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
base
itself
square root
change both terms in order to keep the value the same.

38. Indicates the number of times the base is to be multiplied.
move the decimal point the same number of units to the left
Because 4 multiplied by itself equals 16.
same exponent
exponent

39. To multiply or divide exponent terms that do not have the same base:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Same base
6.74 x 10^-7
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

40. Any number with an exponent of 0 is equal to
must be multiples of 3 or 0
decrease the power-of-10 exponent by the same number of units
1
0

41. A number with an exponent of 2 is often said to be
10^1
squared
3
Subtract the exponent

42. To subtract powers of ten:
10^-2
must be multiples of 3 or 0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
9 (3^2 = 9)

43. 5^1 =
base
5
you have to adjust the value of the exponent in order avoid changing the actual value.
exponent

44. Powers of ten can be added or subtracted only when their exponents
Are Equal
proper scientific
2
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

45. 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
decrease the power-of-10 exponent by the same number of units
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

46. Multiplying by 10
adjust the value of the coefficient
cube root
Moving the decimal point to the right
negative number

47. 3^0 =
1
move the decimal point the same number of units to the right
coefficient
0

48. Step 1: Add the exponents Step 2: Use the common base
3
10^-18
To multiply powers that have the same base:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

49. Valid powers-of-10 for engineering notation
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
must be multiples of 3 or 0
Moving the decimal point to the right

50. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
1
2
To multiply powers that have the same base: