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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. The symbol for the cube root of a number is
cube-root key
the radical sign with a little 3 that indicates the cube root:
0
Subtract the exponent

2. A number - when multiplied by itself - is equal to a given number.
Are Equal
0
square root
change both terms in order to keep the value the same.

3. A number with an exponent of 2 is often said to be
squared
a fractional decimal
0
negative number

4. When you change the position of the decimal point in a coefficient value
you have to adjust the value of the exponent in order avoid changing the actual value.
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
decrease the value of the exponent by 1 (dividing by 10)

5. = 0.01 - or 1 with the decimal point moved two places to the left.
the radical sign with a little 3 that indicates the cube root:
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
change both terms in order to keep the value the same.

6. Dividing by 10
you have to adjust the value of the exponent in order avoid changing the actual value.
coefficient
Moving the decimal point to the left
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

7. 0^5 =
Moving the decimal point to the left
squared
1
0

8. The square root of zero is
change both terms in order to keep the value the same.
5
0
The solution exists - but not in the real number system.

9. A number is a second number which - when multiplied by itself three times - equals the original number.
0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
cube root
one digit to the left of the decimal point

10. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
10^-2
3
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

11. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
10^2
Subtract the exponent
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
radical sign

12. 5^1 =
rewrite one of the terms so that the exponents are equal
one digit to the left of the decimal point
5
1. Divide the coefficients 2. Subtract the exponents

13. 3^0 =
1
5
When moving the decimal point to the left (dividing by 10)
base

14. The square root of 9 is
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
3
Step 1. Divide the coefficients of the terms

15. To multiply or divide exponent terms that do not have the same base:
5
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
2
Engineering notation

16. The cube root of a negative number is also a
10^-18
rewrite one of the terms so that the exponents are equal
negative number
1

17. 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.
the radical sign with a little 3 that indicates the cube root:
When the exponent of a power-of-10 expression is a negative integer:
10^-18
Subtract the exponent

18. Any number with an exponent of 0 is equal to
10^-2
1
rewrite one of the terms so that the exponents are equal
1. Divide the coefficients 2. Subtract the exponents

19. To multiply powers of ten:
Subtract the exponent
1. Multiply the coefficients 2. Add the exponents
2 x 10^9
base

20. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
exponent
rewrite one of the terms so that the exponents are equal
The solution exists - but not in the real number system.

21. 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^-18
The solution exists - but not in the real number system.
1

22. When you move the decimal point in the coefficient to the right
decrease the power-of-10 exponent by the same number of units
a fractional decimal
exponent
Are Equal

23. Negative cube roots are okay ... negative square roots are
Not
proper scientific
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
must be multiples of 3 or 0

24.
cube-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
1. Multiply the coefficients 2. Add the exponents
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

25. 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
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
10^-1
The solution exists - but not in the real number system.

26. Powers of ten can be added or subtracted only when their exponents
radical sign
move the decimal point the same number of units to the right
Are Equal
perfect square

27. A number with an exponent of 3 is often said to be
move the decimal point the same number of units to the left
Engineering notation
cubed
cube root

28. 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
cube root
5
Scientific notation

29. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
Same base
exponent
Are Equal

30. Multiplying by 10
0
Moving the decimal point to the right
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.

31. Numbers with exponents can be directly multiplied or divided only when they have the
Same base
increase the power-of-10 exponent by the same number of units
10^-1
cube-root key

32. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
Same base
10^2
must be multiples of 3 or 0

33. 10 - or 1 with the decimal point moved one place to the right
the radical sign with a little 3 that indicates the cube root:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1
10^1

34. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
0
10^2
To multiply powers that have the same base:

35. For the 10
you have to adjust the value of the exponent in order avoid changing the actual value.
1
exponent
cube root

36. Always 10 for scientific notation
base
cubed
10^-18
same exponent

37. When you move the decimal point in the coefficient to the left
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
you have to adjust the value of the exponent in order avoid changing the actual value.
increase the power-of-10 exponent by the same number of units

38. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
2
Not
itself

39. 1^4 =
1
1. Multiply the coefficients 2. Add the exponents
coefficient
3

40. Increase the value of the exponent by 1 (multiplying by 10)
Same base
When moving the decimal point to the left (dividing by 10)
The solution exists - but not in the real number system.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

41. 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
cubed
exponent
5

42. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
one digit to the left of the decimal point
Not
base

43. A very small number such as 0.000000674 can be written with scientific notation as
Calculator square-root key
decrease the value of the exponent by 1 (dividing by 10)
10^1
6.74 x 10^-7

44. Represents 1 preceded by 17 zeros and a decimal point.
Subtract the exponent
2
Scientific notation
10^-18

45. Indicates the number of times the base is to be multiplied.
squared
exponent
Calculator square-root key
10^1

46. To add or subtract numbers written with exponents:
a fractional decimal
Scientific notation
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
cubed

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
3
adjust the value of the coefficient
1
Scientific notation

48. Step 1: Add the exponents Step 2: Use the common base
move the decimal point the same number of units to the left
2 x 10^9
To multiply powers that have the same base:
10^1

49. The decimal part
proper scientific
coefficient
radical sign
Calculator square-root key

50. The cube root of zero is
exponent
cubed
itself
0