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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. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
1
1
10^-1

2. The cube root of a negative number is also a
negative number
coefficient
cubed
When the exponent of a power-of-10 expression is a negative integer:

3. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
same exponent
change both terms in order to keep the value the same.
10^-1

4. For the 10
exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
When moving the decimal point to the left (dividing by 10)
proper scientific

5. To find the square root of any number - simply key in the number (the radicand) and press the
0
base
Calculator square-root key
When moving the decimal point to the left (dividing by 10)

6. = 0.1 - or 1 with the decimal point moved one place to the left.
Moving the decimal point to the left
10^-1
adjust the value of the coefficient
0

7. When moving the decimal point to the right (multiplying by 10)
Engineering notation
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
0
decrease the value of the exponent by 1 (dividing by 10)

8. The cube root of zero is
0
1 divided by that number with a positive exponent
Scientific notation
3

9. 10 - or 1 with the decimal point moved one place to the right
base
10^1
itself
rewrite one of the terms so that the exponents are equal

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

11. Increase the value of the exponent by 1 (multiplying by 10)
base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
0
When moving the decimal point to the left (dividing by 10)

12.
1
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
Subtract the exponent
Step 1. Divide the coefficients of the terms

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.
negative number
When the exponent of a power-of-10 expression is a negative integer:
1
Scientific notation

14. The square root of zero is
0
Step 1. Divide the coefficients of the terms
change both terms in order to keep the value the same.
cubed

15. To find the cube root of any number - simply key in the number (the radicand) and press cube-root key. On most calculators - the cube-root function is a 2nd level function. This means you have to press the 2nd key before pressing the key for the
decrease the power-of-10 exponent by the same number of units
cube-root key
cube root
9 (3^2 = 9)

16. When you increase the value of the power-of-10 exponent
10^-18
adjust the value of the coefficient
9 (3^2 = 9)
move the decimal point the same number of units to the left

17. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
Step 1. Rewrite each number 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
adjust the value of the coefficient

18. The square of 3 is
9 (3^2 = 9)
Step 1. Divide the coefficients of the terms
Same base
Moving the decimal point to the right

19. 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.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
proper scientific
adjust the value of the coefficient
Engineering notation

20. When the exponents are not 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
exponent
rewrite one of the terms so that the exponents are equal
square root

21. To divide powers of ten:
squared
1. Divide the coefficients 2. Subtract the exponents
When the exponent of a power-of-10 expression is a negative integer:
change both terms in order to keep the value the same.

22. The decimal part
coefficient
itself
10^1
exponent

23. Represents 1 preceded by 17 zeros and a decimal point.
Subtract the exponent
3
Not
10^-18

24. 100 - or 1 with the decimal point moved two places to the right
proper scientific
0
0
10^2

25. Scientific notation requires there to be only
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.
exponent
10^-1
one digit to the left of the decimal point

26. Any number with a negative exponent is equal to
Because 4 multiplied by itself equals 16.
move the decimal point the same number of units to the left
1 divided by that number with a positive exponent
0

27. What number multiplied by itself is equal to 16? The answer is 4. Why?
cube-root key
Because 4 multiplied by itself equals 16.
0
rewrite one of the terms so that the exponents are equal

28. To divide powers that have the same base:
Moving the decimal point to the left
the radical sign with a little 3 that indicates the cube root:
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

29. Indicates the number to be multiplied.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1
3
base

30. To subtract powers of ten:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
coefficient
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

31. Any number with an exponent of 0 is equal to
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
the radical sign with a little 3 that indicates the cube root:
1

32. 3^0 =
1
Moving the decimal point to the left
6.74 x 10^-7
base

33. 1 to any power is equal to
1
Moving the decimal point to the right
exponent
Step 1. Divide the coefficients of the terms

34. 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.
Are Equal
Scientific notation
When the exponent of a power-of-10 expression is a negative integer:
increase the power-of-10 exponent by the same number of units

35. The square root of 9 is
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
3
0
exponent

36. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Calculator square-root key
10^2
a fractional decimal
5

37. Numbers with exponents can be directly multiplied or divided only when they have the
2
Same base
0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

38. The symbol for the cube root of a number is
decrease the value of the exponent by 1 (dividing by 10)
negative number
To multiply powers that have the same base:
the radical sign with a little 3 that indicates the cube root:

39. There are no special rules for adding and subtracting numbers that are written with exponents.
1 divided by that number with a positive exponent
10^-18
change both terms in order to keep the value the same.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

40. To multiply powers of 10:
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.
10^-18
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

41. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^2
1
change both terms in order to keep the value the same.

42. Dividing by 10
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
rewrite one of the terms so that the exponents are equal
Moving the decimal point to the left
1

43. 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.
10^2
perfect square
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
increase the power-of-10 exponent by the same number of units

44. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
2
9 (3^2 = 9)
Engineering notation

45. Indicates the number of times the base is to be multiplied.
exponent
itself
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1

46. 1 to any power is equal to
Scientific notation
Not
1
2

47. Powers of ten can be added or subtracted only when their exponents
Are Equal
cube-root key
square root
Calculator square-root key

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.
1
radical sign
Not
squared

49. When you move the decimal point in the coefficient to the right
1
0
decrease the power-of-10 exponent by the same number of units
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

50. Valid powers-of-10 for engineering notation
When the exponent of a power-of-10 expression is a negative integer:
1
must be multiples of 3 or 0
5