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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. 1^4 =
1
same exponent
Subtract the exponent
9 (3^2 = 9)

2. Any number with an exponent of 1 is equal to
square root
10^2
itself
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

3. Step 1: Add the exponents Step 2: Use the common base
1. Multiply the coefficients 2. Add the exponents
1
To multiply powers that have the same base:
Same base

4. 1 to any power is equal to
Scientific notation
1
change both terms in order to keep the value the same.
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

5. To multiply powers of 10:
Engineering notation
1
Step 1. Divide the coefficients of the terms
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.

6. To subtract powers of ten:
Subtract the exponent
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

7. When you increase the value of the power-of-10 exponent
When moving the decimal point to the left (dividing by 10)
the radical sign with a little 3 that indicates the cube root:
move the decimal point the same number of units to the left
a fractional decimal

8. Represents 1 preceded by 17 zeros and a decimal point.
cubed
2
To multiply powers that have the same base:
10^-18

9. The square root of 9 is
Are Equal
To multiply powers that have the same base:
3
10^-2

10. The cube root of a negative number is also a
Moving the decimal point to the left
base
negative number
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

11. To divide powers that have the same base:
Not
0
6.74 x 10^-7
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

12. Allows you to express very large and very small numbers without using large numbers of digits and decimal places. It's all done with powers 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.
Scientific notation
cube-root key
When moving the decimal point to the left (dividing by 10)

13. 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.
decrease the power-of-10 exponent by the same number of units
1
coefficient
When the exponent of a power-of-10 expression is a negative integer:

14. Dividing by 10
Step 1. Divide the coefficients of the terms
cube-root key
Moving the decimal point to the left
rewrite one of the terms so that the exponents are equal

15.
the radical sign with a little 3 that indicates the cube root:
decrease the value of the exponent by 1 (dividing by 10)
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

16. Valid powers-of-10 for engineering notation
1. Multiply the coefficients 2. Add the exponents
increase the power-of-10 exponent by the same number of units
must be multiples of 3 or 0
10^2

17. To add powers of ten:
cube-root key
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0
10^-18

18. The decimal part
coefficient
1. Divide the coefficients 2. Subtract the exponents
the radical sign with a little 3 that indicates the cube root:
itself

19. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
10^-18
base
increase the power-of-10 exponent by the same number of units

20. Multiplying by 10
coefficient
2 x 10^9
Moving the decimal point to the right
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

21. A very small number such as 0.000000674 can be written with scientific notation as
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
6.74 x 10^-7
you have to adjust the value of the exponent in order avoid changing the actual value.
negative number

22. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
the radical sign with a little 3 that indicates the cube root:
1. Divide the coefficients 2. Subtract the exponents
1

23. 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.
radical sign
same exponent
Subtract the 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

24. 3^0 =
decrease the power-of-10 exponent by the same number of units
1. Divide the coefficients 2. Subtract the exponents
10^2
1

25. A number - when multiplied by itself - is equal to a given number.
1
square root
Moving the decimal point to the right
a fractional decimal

26. To divide powers of 10:
Step 1. Divide the coefficients of the terms
Same base
5
Subtract the exponent

27. When the exponents are not the same
6.74 x 10^-7
decrease the value of the exponent by 1 (dividing by 10)
1
rewrite one of the terms so that the exponents are equal

28. The cube root of zero is
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0
a fractional decimal
cubed

29. A number with an exponent of 2 is often said to be
squared
radical sign
10^-2
1

30. Indicates the number of times the base is to be multiplied.
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
exponent
itself
10^-18

31. Negative cube roots are okay ... negative square roots are
1. Divide the coefficients 2. Subtract the exponents
Not
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-1

32. When you decrease the value of the power-of-10 exponent
decrease the value of the exponent by 1 (dividing by 10)
increase the power-of-10 exponent by the same number of units
move the decimal point the same number of units to the right
When the exponent of a power-of-10 expression is a negative integer:

33. 10 - or 1 with the decimal point moved one place to the right
10^1
Because 4 multiplied by itself equals 16.
The solution exists - but not in the real number system.
move the decimal point the same number of units to the right

34. 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
When moving the decimal point to the left (dividing by 10)
change both terms in order to keep the value the same.
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

35. To find the square root of any number - simply key in the number (the radicand) and press the
Engineering notation
exponent
Calculator square-root key
square root

36. Any number with a negative exponent is equal to
Engineering notation
10^2
coefficient
1 divided by that number with a positive exponent

37. 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
square root
1. Multiply the coefficients 2. Add the exponents
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

38. Always 10 for scientific notation
10^2
base
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
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

39. Indicates the number to be multiplied.
1. Multiply the coefficients 2. Add the exponents
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left
base

40. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
10^-1
Calculator square-root key
adjust the value of the coefficient

41. 5^1 =
negative number
5
cube root
increase the power-of-10 exponent by the same number of units

42. Any number with an exponent of 0 is equal to
1
Moving the decimal point to the right
Are Equal
same exponent

43. The square of 3 is
negative number
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-1
9 (3^2 = 9)

44. The square root of zero is
perfect square
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1
0

45. A number is a second number which - when multiplied by itself three times - equals the original number.
10^1
decrease the power-of-10 exponent by the same number of units
cubed
cube root

46. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
change both terms in order to keep the value the same.
itself
Engineering notation
Subtract the exponent

47. To divide powers of ten:
adjust the value of the coefficient
must be multiples of 3 or 0
1. Divide the coefficients 2. Subtract the exponents
increase the power-of-10 exponent by the same number of units

48. 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.
you have to adjust the value of the exponent in order avoid changing the actual value.
10^-18
Same base
perfect square

49. The symbol for the cube root of a number is
itself
move the decimal point the same number of units to the left
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.

50. Numbers with exponents can be directly multiplied or divided only when they have the
0
10^-18
Scientific notation
Same base