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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. For the 10
10^2
cube root
exponent
same exponent

2. 1 to any power is equal to
2
perfect square
10^-2
1

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

4. To find the square root of any number - simply key in the number (the radicand) and press the
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
adjust the value of the coefficient
Calculator square-root key
base

5. To multiply powers of 10:
10^2
10^1
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.
decrease the power-of-10 exponent by the same number of units

6. 1^4 =
must be multiples of 3 or 0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Subtract the exponent
1

7. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
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.
0

8. The square root of 9 is
base
3
move the decimal point the same number of units to the left
9 (3^2 = 9)

9. To add or subtract numbers written with exponents:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
exponent
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
When moving the decimal point to the left (dividing by 10)

10. Multiplying by 10
1
proper scientific
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 right

11. 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:
Scientific notation
Same base
6.74 x 10^-7

12. A number - when multiplied by itself - is equal to a given number.
When moving the decimal point to the left (dividing by 10)
same exponent
square root
Moving the decimal point to the right

13. The square of 3 is
base
cube root
9 (3^2 = 9)
Are Equal

14. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Are Equal
move the decimal point the same number of units to the right
a fractional decimal
10^2

15. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
move the decimal point the same number of units to the left
Subtract the exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

16. The symbol for the cube root of a number is
decrease the value of the exponent by 1 (dividing by 10)
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
same exponent
the radical sign with a little 3 that indicates the cube root:

17. Step 1: Add the exponents Step 2: Use the common base
1. Multiply the coefficients 2. Add the exponents
To multiply powers that have the same base:
Engineering notation
10^-2

18. 5^1 =
5
a fractional decimal
When the exponent of a power-of-10 expression is a negative integer:
1. Divide the coefficients 2. Subtract the exponents

19. 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
Scientific notation
10^1
adjust the value of the coefficient
perfect square

20. Indicates the number of times the base is to be multiplied.
1
exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Same base

21. When moving the decimal point to the right (multiplying by 10)
one digit to the left of the decimal point
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
exponent
decrease the value of the exponent by 1 (dividing by 10)

22. A number with an exponent of 3 is often said to be
6.74 x 10^-7
0
1
cubed

23. 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
same exponent
Moving the decimal point to the left
coefficient
When the exponent of a power-of-10 expression is a negative integer:

24. To multiply or divide exponent terms that do not have the same base:
1 divided by that number with a positive exponent
you have to adjust the value of the exponent in order avoid changing the actual value.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
change both terms in order to keep the value the same.

25. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
When the exponent of a power-of-10 expression is a negative integer:
1
move the decimal point the same number of units to the right

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

27. 100 - or 1 with the decimal point moved two places to the right
Subtract the exponent
10^2
itself
1. Divide the coefficients 2. Subtract the exponents

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

29. When you move the decimal point in the coefficient to the right
exponent
9 (3^2 = 9)
cube-root key
decrease the power-of-10 exponent by the same number of units

30. 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.
Moving the decimal point to the left
Engineering notation
1. Multiply the coefficients 2. Add the exponents
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

31. 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
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1. Divide the coefficients 2. Subtract the exponents
change both terms in order to keep the value the same.
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

32. When you increase the value of the power-of-10 exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the left
Step 1. Divide the coefficients of the terms
When moving the decimal point to the left (dividing by 10)

33. 1 to any power is equal to
cubed
1
Moving the decimal point to the left
Same base

34. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
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
radical sign
Calculator square-root key

35. Powers of ten can be added or subtracted only when their exponents
10^2
you have to adjust the value of the exponent in order avoid changing the actual value.
Moving the decimal point to the right
Are Equal

36. When the exponents are not the same
perfect square
The solution exists - but not in the real number system.
Calculator square-root key
rewrite one of the terms so that the exponents are equal

37.
10^-18
10^-2
Calculator square-root key
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

38. 0 to any power is equal to
proper scientific
The solution exists - but not in the real number system.
0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

39. The cube root of zero is
1
0
Not
move the decimal point the same number of units to the left

40. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
2 x 10^9
itself
1

41. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
To multiply powers that have the same base:
itself
Not

42. 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
Because 4 multiplied by itself equals 16.
square root
Scientific 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

43. To multiply powers of ten:
cubed
10^2
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
1. Multiply the coefficients 2. Add the exponents

44. 3^0 =
10^-1
1
Step 1. Divide the coefficients of the terms
Calculator square-root key

45. A very small number such as 0.000000674 can be written with scientific notation as
proper scientific
you have to adjust the value of the exponent in order avoid changing the actual value.
exponent
6.74 x 10^-7

46. Any number with an exponent of 1 is equal to
itself
Moving the decimal point to the left
proper scientific
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

47. Scientific notation requires there to be only
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
one digit to the left of the decimal point
increase the power-of-10 exponent by the same number of units
the radical sign with a little 3 that indicates the cube root:

48. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
one digit to the left of the decimal point
you have to adjust the value of the exponent in order avoid changing the actual value.
Engineering notation

49. To divide powers of 10:
Step 1. Divide the coefficients of the terms
1
2
you have to adjust the value of the exponent in order avoid changing the actual value.

50. 10 - or 1 with the decimal point moved one place to the right
move the decimal point the same number of units to the right
cube-root key
10^1
base