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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?
Are Equal
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Subtract the exponent

2. A number is a second number which - when multiplied by itself three times - equals the original number.
you have to adjust the value of the exponent in order avoid changing the actual value.
cube root
perfect square
10^-2

3. Indicates the number to be multiplied.
3
10^1
10^-1
base

4. To subtract powers of ten:
To multiply powers that have the same base:
base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
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. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
square root
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
proper scientific
2 x 10^9

6. When you move the decimal point in the coefficient to the left
0
the radical sign with a little 3 that indicates the cube root:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
increase the power-of-10 exponent by the same number of units

7. Multiplying by 10
exponent
Engineering notation
Moving the decimal point to the right
one digit to the left of the decimal point

8. Valid powers-of-10 for engineering notation
base
negative number
proper scientific
must be multiples of 3 or 0

9. 1^4 =
proper scientific
square root
coefficient
1

10. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
0
The solution exists - but not in the real number system.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

11. To multiply 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
10^1
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
1. Multiply the coefficients 2. Add the exponents

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.
0
Scientific notation
1
5

13. What number multiplied by itself is equal to 16? The answer is 4. Why?
the radical sign with a little 3 that indicates the cube root:
Because 4 multiplied by itself equals 16.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
When the exponent of a power-of-10 expression is a negative integer:

14. Always 10 for scientific notation
0
base
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

15. Negative cube roots are okay ... negative square roots are
10^-2
rewrite one of the terms so that the exponents are equal
Not
you have to adjust the value of the exponent in order avoid changing the actual value.

16. A number - when multiplied by itself - is equal to a given number.
1
square root
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
proper scientific

17. Powers of ten can be added or subtracted only when their exponents
Engineering notation
Are Equal
Subtract the exponent
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.

18. 100 - or 1 with the decimal point moved two places to the right
10^2
2
9 (3^2 = 9)
negative number

19. 10 - or 1 with the decimal point moved one place to the right
decrease the value of the exponent by 1 (dividing by 10)
Calculator square-root key
proper scientific
10^1

20. 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 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
10^2
a fractional decimal
decrease the power-of-10 exponent by the same number of units

21. 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
negative number
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
adjust the value of the coefficient
10^-2

22. Any number with a negative exponent is equal to
10^-2
proper scientific
1 divided by that number with a positive exponent
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

23. 1 to any power is equal to
move the decimal point the same number of units to the left
Are Equal
itself
1

24. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
must be multiples of 3 or 0
10^-1

25. To multiply powers of 10:
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.
The solution exists - but not in the real number system.
3
0

26. When you increase the value of the power-of-10 exponent
you have to adjust the value of the exponent in order avoid changing the actual value.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
move the decimal point the same number of units to the right
move the decimal point the same number of units to the left

27. 0^5 =
0
2
Subtract the exponent
base

28. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
When the exponent of a power-of-10 expression is a negative integer:
10^1
1. Multiply the coefficients 2. Add the exponents

29. To multiply or divide exponent terms that do not have the same base:
same exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Calculator square-root key

30. The symbol for the cube root of a number is
1. Multiply the coefficients 2. Add the exponents
the radical sign with a little 3 that indicates the cube root:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^-18

31. 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
1
Not
a fractional decimal

32. When you change the position of the decimal point in a coefficient value
Moving the decimal point to the right
Same base
To multiply powers that have the same base:
you have to adjust the value of the exponent in order avoid changing the actual value.

33. Indicates the number of times the base is to be multiplied.
1. Multiply the coefficients 2. Add the exponents
exponent
negative number
0

34. The decimal part
base
coefficient
rewrite one of the terms so that the exponents are equal
perfect square

35. 5^1 =
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
5
must be multiples of 3 or 0
9 (3^2 = 9)

36. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
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.
proper scientific
Not

37. 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.
1
Subtract the exponent
When moving the decimal point to the left (dividing by 10)
When the exponent of a power-of-10 expression is a negative integer:

38. To divide powers of ten:
you have to adjust the value of the exponent in order avoid changing the actual value.
itself
1. Divide the coefficients 2. Subtract the exponents
coefficient

39. 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
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
cube-root key
10^-18

40. 3^0 =
1
Step 1. Divide the coefficients of the terms
When the exponent of a power-of-10 expression is a negative integer:
1. Divide the coefficients 2. Subtract the exponents

41. The cube root of a negative number is also a
2 x 10^9
1. Divide the coefficients 2. Subtract the exponents
Moving the decimal point to the left
negative number

42. The square root of zero is
1
you have to adjust the value of the exponent in order avoid changing the actual value.
Moving the decimal point to the right
0

43. 0 to any power is equal to
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Moving the decimal point to the left
1
0

44. = 0.01 - or 1 with the decimal point moved two places to the left.
must be multiples of 3 or 0
10^2
one digit to the left of the decimal point
10^-2

45. When moving the decimal point to the right (multiplying by 10)
10^-18
decrease the value of the exponent by 1 (dividing by 10)
squared
1

46. When the exponents are not the same
Subtract the exponent
When the exponent of a power-of-10 expression is a negative integer:
exponent
rewrite one of the terms so that the exponents are equal

47. 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
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. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
negative number

48. Numbers with exponents can be directly multiplied or divided only when they have the
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
move the decimal point the same number of units to the right
When moving the decimal point to the left (dividing by 10)
Same base

49. = 0.1 - or 1 with the decimal point moved one place to the left.
exponent
10^-1
you have to adjust the value of the exponent in order avoid changing the actual value.
change both terms in order to keep the value the same.

50. Increase the value of the exponent by 1 (multiplying by 10)
1 divided by that number with a positive exponent
When moving the decimal point to the left (dividing by 10)
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
cube-root key