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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. 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.
1. Divide the coefficients 2. Subtract the exponents
1
Engineering notation
10^-1

2. Always 10 for scientific notation
cube-root key
base
1
itself

3. To subtract powers of ten:
10^-2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-1
cube-root key

4. To multiply powers of 10:
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.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
same exponent
When moving the decimal point to the left (dividing by 10)

5. Valid powers-of-10 for 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
2 x 10^9
must be multiples of 3 or 0
cube-root key

6. Scientific notation requires there to be only
Not
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
one digit to the left of the decimal point
cube root

7. When you move the decimal point in the coefficient to the right
1
decrease the power-of-10 exponent by the same number of units
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1. Multiply the coefficients 2. Add the exponents

8. Powers of ten can be added or subtracted only when their exponents
Scientific notation
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.
Are Equal

9. 1 to any power is equal to
Moving the decimal point to the left
Scientific notation
you have to adjust the value of the exponent in order avoid changing the actual value.
1

10. The decimal part
coefficient
2
Moving the decimal point to the right
Calculator square-root key

11. The square of 3 is
9 (3^2 = 9)
squared
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
0

12. 1^4 =
When the exponent of a power-of-10 expression is a negative integer:
1
square root
negative number

13. Valid powers of 10 for engineering notation are:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
exponent
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

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

15. To divide powers that have the same base:
1. Divide the coefficients 2. Subtract the exponents
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.
change both terms in order to keep the value the same.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

16. 100 - or 1 with the decimal point moved two places to the right
10^2
coefficient
decrease the power-of-10 exponent by the same number of units
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

17. Negative cube roots are okay ... negative square roots are
one digit to the left of the decimal point
Not
square root
negative number

18. When you change the position of the decimal point in a coefficient value
increase the power-of-10 exponent by the same number of units
you have to adjust the value of the exponent in order avoid changing the actual value.
decrease the power-of-10 exponent by the same number of units
3

19. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
same exponent
2 x 10^9
Subtract the exponent

20. Indicates the number to be multiplied.
proper scientific
base
When moving the decimal point to the left (dividing by 10)
0

21. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
radical sign
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
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

22. Step 1: Add the exponents Step 2: Use the common base
10^1
proper scientific
To multiply powers that have the same base:
radical sign

23. 0 to any power is equal to
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.
0
10^1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

24. The symbol for the cube root of a number is
you have to adjust the value of the exponent in order avoid changing the actual value.
To multiply powers that have the same base:
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
the radical sign with a little 3 that indicates the cube root:

25. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
Same base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
0

26. Multiplying by 10
Moving the decimal point to the right
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Divide the coefficients of the terms
1

27. 5^1 =
Same base
When moving the decimal point to the left (dividing by 10)
10^1
5

28. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
2
10^-18

29. 1 to any power is equal to
square root
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.
same exponent

30. 0^5 =
move the decimal point the same number of units to the right
1
0
10^2

31. The cube root of a negative number is also a
negative number
adjust the value of the coefficient
rewrite one of the terms so that the exponents are equal
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

32. To add powers of ten:
1 divided by that number with a positive exponent
6.74 x 10^-7
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the left

33. The square root of 9 is
cube-root key
3
base
you have to adjust the value of the exponent in order avoid changing the actual value.

34. 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.
To multiply powers that have the same base:
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
radical sign

35. = 0.01 - or 1 with the decimal point moved two places to the left.
1. Multiply the coefficients 2. Add the exponents
1
10^-2
Not

36.
1
5
Engineering notation
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

37. Any number with a negative exponent is equal to
Step 1. Divide the coefficients of the terms
perfect square
Moving the decimal point to the right
1 divided by that number with a positive exponent

38. Dividing by 10
must be multiples of 3 or 0
1
Moving the decimal point to the left
square root

39. When you decrease the value of the power-of-10 exponent
Scientific notation
10^-1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
move the decimal point the same number of units to the right

40. For the 10
Not
exponent
move the decimal point the same number of units to the right
Are Equal

41. When the exponents are not the same
Not
rewrite one of the terms so that the exponents are equal
Step 1. Divide the coefficients of the terms
decrease the value of the exponent by 1 (dividing by 10)

42. = 0.1 - or 1 with the decimal point moved one place to the left.
Moving the decimal point to the right
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
10^-1
2 x 10^9

43. To add or subtract numbers written with exponents:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
base
proper scientific
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

44. 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.
3
perfect square
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

45. When you move the decimal point in the coefficient to the left
1
the radical sign with a little 3 that indicates the cube root:
10^1
increase the power-of-10 exponent by the same number of units

46. 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
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
0
increase the power-of-10 exponent by the same number of units

47. Represents 1 preceded by 17 zeros and a decimal point.
6.74 x 10^-7
1
10^-18
10^2

48. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
1
move the decimal point the same number of units to the right
Scientific notation

49. The cube root of zero is
squared
10^2
coefficient
0

50. To find the square root of any number - simply key in the number (the radicand) and press the
decrease the value of the exponent by 1 (dividing by 10)
Calculator square-root key
must be multiples of 3 or 0
Scientific notation