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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. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
cubed
2 x 10^9
Subtract the exponent
move the decimal point the same number of units to the left

2.
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
squared
6.74 x 10^-7
The solution exists - but not in the real number system.

3. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
negative number
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

4. The square root of zero is
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.
squared
Because 4 multiplied by itself equals 16.
0

5. Any number with a negative exponent is equal to
6.74 x 10^-7
square root
1 divided by that number with a positive exponent
1

6. 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.
2
Engineering notation
0
When moving the decimal point to the left (dividing by 10)

7. A number with an exponent of 3 is often said to be
the radical sign with a little 3 that indicates the cube root:
base
cubed
0

8. To subtract powers of ten:
decrease the value of the exponent by 1 (dividing by 10)
perfect square
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-2

9. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
radical sign
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Moving the decimal point to the left

10. 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.
1
When the exponent of a power-of-10 expression is a negative integer:
10^-18
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

11. A very small number such as 0.000000674 can be written with scientific notation as
increase the power-of-10 exponent by the same number of units
6.74 x 10^-7
perfect square
cube root

12. 1 to any power is equal to
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Calculator square-root key
1
Are Equal

13. 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
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^2
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
Moving the decimal point to the left

14. The cube root of zero is
10^-1
move the decimal point the same number of units to the left
one digit to the left of the decimal point
0

15. To add powers of ten:
10^-2
10^1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
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.

16. When you change the position of the decimal point in a coefficient value
5
When moving the decimal point to the left (dividing by 10)
you have to adjust the value of the exponent in order avoid changing the actual value.
0

17. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
Calculator square-root key
5
move the decimal point the same number of units to the left

18. The square root of 9 is
1. Divide the coefficients 2. Subtract the exponents
9 (3^2 = 9)
decrease the value of the exponent by 1 (dividing by 10)
3

19. When you move the decimal point in the coefficient to the left
decrease the value of the exponent by 1 (dividing by 10)
3
1
increase the power-of-10 exponent by the same number of units

20. 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.
Moving the decimal point to the left
10^2
increase the power-of-10 exponent by the same number of units

21. Don't bother trying to find the square root of a negative number.
a fractional decimal
must be multiples of 3 or 0
1
The solution exists - but not in the real number system.

22. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
2
Subtract the exponent
10^2
6.74 x 10^-7

23. 0^5 =
one digit to the left of the decimal point
base
change both terms in order to keep the value the same.
0

24. For the 10
coefficient
1
When moving the decimal point to the left (dividing by 10)
exponent

25. There are no special rules for adding and subtracting numbers that are written with exponents.
move the decimal point the same number of units to the right
5
move the decimal point the same number of units to the left
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

26. 10 - or 1 with the decimal point moved one place to the right
10^1
1 divided by that number with a positive exponent
base
1. Divide the coefficients 2. Subtract the exponents

27. To divide powers that have the same base:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
0
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

28. = 0.1 - or 1 with the decimal point moved one place to the left.
1 divided by that number with a positive exponent
10^-1
adjust the value of the coefficient
Are Equal

29. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
0
0
Step 1. Divide the coefficients of the terms
proper scientific

30. The symbol for the cube root of a number is
10^-18
the radical sign with a little 3 that indicates the cube root:
0
base

31. To divide powers of 10:
Step 1. Divide the coefficients of the terms
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
The solution exists - but not in the real number system.

32. 0 to any power is equal to
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Moving the decimal point to the right
must be multiples of 3 or 0
0

33. Indicates the number of times the base is to be multiplied.
1
0
exponent
When the exponent of a power-of-10 expression is a negative integer:

34. To add or subtract numbers written with exponents:
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
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

35. Negative cube roots are okay ... negative square roots are
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
rewrite one of the terms so that the exponents are equal
Not
cubed

36. Any number with an exponent of 1 is equal to
Because 4 multiplied by itself equals 16.
itself
1
exponent

37. 100 - or 1 with the decimal point moved two places to the right
To multiply powers that have the same base:
Are Equal
10^2
square root

38. 1 to any power is equal to
1
must be multiples of 3 or 0
To multiply powers that have the same base:
decrease the value of the exponent by 1 (dividing by 10)

39. To multiply or divide exponent terms that do not have the same base:
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.
square root
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

40. Adding and subtracting powers of ten can be a bit more complicated than multiplying and dividing. The main problem is that powers of ten can be added or subtracted only when both terms have the
change both terms in order to keep the value the same.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
coefficient
same exponent

41. To find the square root of any number - simply key in the number (the radicand) and press the
10^-18
1
Because 4 multiplied by itself equals 16.
Calculator square-root key

42. 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.
When the exponent of a power-of-10 expression is a negative integer:
perfect square
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.
10^2

43. = 0.01 - or 1 with the decimal point moved two places to the left.
When moving the decimal point to the left (dividing by 10)
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^-2
must be multiples of 3 or 0

44. Indicates the number to be multiplied.
5
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
Moving the decimal point to the right

45. To multiply powers of 10:
Because 4 multiplied by itself equals 16.
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.
5
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

46. 1^4 =
0
1
10^-2
cubed

47. When you increase the value of the power-of-10 exponent
squared
1
square root
move the decimal point the same number of units to the left

48. 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.
cube root
1
Calculator square-root key
radical sign

49. To multiply powers of ten:
Moving the decimal point to the left
1. Multiply the coefficients 2. Add the exponents
0
one digit to the left of the decimal point

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