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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. = 0.01 - or 1 with the decimal point moved two places to the left.
Subtract the exponent
move the decimal point the same number of units to the right
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-2

2. There are no special rules for adding and subtracting numbers that are written with exponents.
negative number
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^2
To multiply powers that have the same base:

3. 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.
move the decimal point the same number of units to the left
base
radical sign
one digit to the left of the decimal point

4. A number with an exponent of 2 is often said to be
squared
0
exponent
Step 1. Divide the coefficients of the terms

5. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
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.
negative number

6. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
0
the radical sign with a little 3 that indicates the cube root:
1

7. When you decrease the value of the power-of-10 exponent
negative number
move the decimal point the same number of units to the right
1
one digit to the left of the decimal point

8. 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
base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
change both terms in order to keep the value the same.
Calculator square-root key

9. Scientific notation requires there to be only
one digit to the left of the decimal point
10^-18
Moving the decimal point to the right
Subtract the exponent

10. The cube root of zero is
0
base
Not
proper scientific

11. 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
adjust the value of the coefficient
squared
Same base
change both terms in order to keep the value the same.

12. 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
0
exponent
Because 4 multiplied by itself equals 16.

13. The symbol for the cube root of a number is
1 divided by that number with a positive exponent
adjust the value of the coefficient
base
the radical sign with a little 3 that indicates the cube root:

14. 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.
exponent
1
rewrite one of the terms so that the exponents are equal

15. Indicates the number of times the base is to be multiplied.
one digit to the left of the decimal point
exponent
negative number
10^-2

16. To multiply powers of 10:
Moving the decimal point to the left
0
Calculator square-root key
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.

17. The decimal part
10^-1
1
coefficient
proper scientific

18. 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.
0
decrease the power-of-10 exponent by the same number of units
Scientific notation
The solution exists - but not in the real number system.

19. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
same exponent
10^-1
Subtract the exponent
0

20. 0 to any power is equal to
radical sign
0
move the decimal point the same number of units to the right
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

21. When you move the decimal point in the coefficient to the right
decrease the power-of-10 exponent by the same number of units
perfect square
exponent
Same base

22. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
Calculator square-root key
0
2 x 10^9

23. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
Moving the decimal point to the right
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
exponent

24. A number - when multiplied by itself - is equal to a given number.
10^-18
2 x 10^9
the radical sign with a little 3 that indicates the cube root:
square root

25. Indicates the number to be multiplied.
coefficient
0
base
9 (3^2 = 9)

26. Numbers with exponents can be directly multiplied or divided only when they have the
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Same base
Not

27. Don't bother trying to find the square root of a negative number.
10^1
decrease the value of the exponent by 1 (dividing by 10)
The solution exists - but not in the real number system.
When moving the decimal point to the left (dividing by 10)

28. To add or subtract numbers written with exponents:
1. Multiply the coefficients 2. Add the exponents
negative number
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

29. 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.
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
coefficient
radical sign

30. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Because 4 multiplied by itself equals 16.
proper scientific
10^1
2 x 10^9

31. Powers of ten can be added or subtracted only when their exponents
Subtract the exponent
1. Divide the coefficients 2. Subtract the exponents
Are Equal
Scientific notation

32. 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.
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.
Engineering notation
radical sign

33. When the exponents are not the same
move the decimal point the same number of units to the left
rewrite one of the terms so that the exponents are equal
The solution exists - but not in the real number system.
Subtract the exponent

34. 100 - or 1 with the decimal point moved two places to the right
square root
Are Equal
10^2
2

35. Any number with an exponent of 1 is equal to
9 (3^2 = 9)
itself
cube root
negative number

36. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
6.74 x 10^-7
perfect square
When moving the decimal point to the left (dividing by 10)

37. To divide powers that have the same base:
1
squared
1. Divide the coefficients 2. Subtract the exponents
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

38. Valid powers-of-10 for engineering notation
Not
increase the power-of-10 exponent by the same number of units
Step 1. Divide the coefficients of the terms
must be multiples of 3 or 0

39. Dividing by 10
Moving the decimal point to the left
0
exponent
1

40. The square of 3 is
2
5
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.
9 (3^2 = 9)

41. To add powers of ten:
negative number
base
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the left

42.
exponent
square root
perfect square
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

43. To multiply powers of ten:
When moving the decimal point to the left (dividing by 10)
cube root
10^1
1. Multiply the coefficients 2. Add the exponents

44. 1 to any power is equal to
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
negative number
10^1

45. When you move the decimal point in the coefficient to the left
Subtract the exponent
increase the power-of-10 exponent by the same number of units
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Calculator square-root key

46. A number is a second number which - when multiplied by itself three times - equals the original number.
square root
cube root
1
coefficient

47. 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.
base
1
perfect square
When moving the decimal point to the left (dividing by 10)

48. A negative exponent does not mean the decimal value is negative. It means the decimal value is
0
3
5
a fractional decimal

49. 0^5 =
1
0
exponent
a fractional decimal

50. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
move the decimal point the same number of units to the left
perfect square
Moving the decimal point to the left