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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.
10^-2
decrease the power-of-10 exponent by the same number of units
0
2 x 10^9

2. The square of 3 is
9 (3^2 = 9)
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
10^-2
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

3. To divide powers of 10:
base
2
0
Step 1. Divide the coefficients of the terms

4. 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.
Engineering notation
Not
9 (3^2 = 9)

5. 100 - or 1 with the decimal point moved two places 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
10^2
cube-root key
Moving the decimal point to the left

6. 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
move the decimal point the same number of units to the left
1. Divide the coefficients 2. Subtract the exponents
square root

7. When you move the decimal point in the coefficient to the right
0
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.
decrease the power-of-10 exponent by the same number of units
0

8. Step 1: Add the exponents Step 2: Use the common base
0
squared
1
To multiply powers that have the same base:

9. Dividing by 10
Moving the decimal point to the left
cubed
10^2
square root

10. The decimal part
1 divided by that number with a positive exponent
proper scientific
Because 4 multiplied by itself equals 16.
coefficient

11. 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
change both terms in order to keep the value the same.
1. Divide the coefficients 2. Subtract the exponents
perfect square
10^2

12. 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
itself
1
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
negative number

13. = 0.1 - or 1 with the decimal point moved one place to the left.
itself
10^-1
Scientific notation
1

14. When you move the decimal point in the coefficient to the left
1
Same base
Moving the decimal point to the right
increase the power-of-10 exponent by the same number of units

15. 5^1 =
Scientific notation
perfect square
5
you have to adjust the value of the exponent in order avoid changing the actual value.

16. 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
Are Equal
perfect square
change both terms in order to keep the value the same.

17. The square root of zero is
6.74 x 10^-7
0
1
To multiply powers that have the same base:

18. When you decrease the value of the power-of-10 exponent
9 (3^2 = 9)
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
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the right

19. When the exponents are not the same
you have to adjust the value of the exponent in order avoid changing the actual value.
rewrite one of the terms so that the exponents are equal
increase the power-of-10 exponent by the same number of units
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

20. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Subtract the exponent
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
0

21. 1 to any power is equal to
exponent
0
1
10^-1

22. A number with an exponent of 2 is often said to be
Same base
change both terms in order to keep the value the same.
10^-18
squared

23. For the 10
perfect square
Are Equal
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
exponent

24. Any number with an exponent of 1 is equal to
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^-2
itself
0

25. 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.
2 x 10^9
negative number
Because 4 multiplied by itself equals 16.
When the exponent of a power-of-10 expression is a negative integer:

26. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
change both terms in order to keep the value the same.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
2 x 10^9
a fractional decimal

27. 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.
When the exponent of a power-of-10 expression is a negative integer:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Subtract the exponent

28. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
rewrite one of the terms so that the exponents are equal
Step 1. Divide the coefficients of the terms
exponent
proper scientific

29. Multiplying by 10
1
Calculator square-root key
3
Moving the decimal point to the right

30. Always 10 for scientific notation
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1
base

31. 0 to any power is equal to
Not
0
10^-2
cube root

32. Indicates the number to be multiplied.
one digit to the left of the decimal point
adjust the value of the coefficient
base
1. Divide the coefficients 2. Subtract the exponents

33. To divide powers of ten:
0
base
1. Divide the coefficients 2. Subtract the exponents
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

34. The square root of 9 is
decrease the power-of-10 exponent by the same number of units
3
10^-2
Subtract the exponent

35. To add powers of ten:
Calculator square-root key
Because 4 multiplied by itself equals 16.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1 divided by that number with a positive exponent

36. To multiply or divide exponent terms that do not have the same base:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
3
increase the power-of-10 exponent by the same number of units
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

37. What number multiplied by itself is equal to 16? The answer is 4. Why?
Moving the decimal point to the right
cube-root key
coefficient
Because 4 multiplied by itself equals 16.

38. When moving the decimal point to the right (multiplying by 10)
Because 4 multiplied by itself equals 16.
proper scientific
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
decrease the value of the exponent by 1 (dividing by 10)

39. To multiply powers of ten:
1
1. Multiply the coefficients 2. Add the exponents
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.
rewrite one of the terms so that the exponents are equal

40. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
rewrite one of the terms so that the exponents are equal
Moving the decimal point to the right
move the decimal point the same number of units to the left

41. 1 to any power is equal to
1
a fractional decimal
Moving the decimal point to the right
proper scientific

42. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
you have to adjust the value of the exponent in order avoid changing the actual value.
1 divided by that number with a positive exponent
When moving the decimal point to the left (dividing by 10)

43. Valid powers-of-10 for engineering notation
1. Multiply the coefficients 2. Add the exponents
10^-1
must be multiples of 3 or 0
10^2

44. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Calculator square-root key
Because 4 multiplied by itself equals 16.
itself
a fractional decimal

45. When you increase the value of the power-of-10 exponent
1
decrease the power-of-10 exponent by the same number of units
When the exponent of a power-of-10 expression is a negative integer:
move the decimal point the same number of units to the left

46. 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
Engineering notation
10^2

47. 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.
Scientific notation
must be multiples of 3 or 0
2
6.74 x 10^-7

48. 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.
one digit to the left of the decimal point
1
2 x 10^9

49. The cube root of a negative number is also a
increase the power-of-10 exponent by the same number of units
10^-1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
negative number

50. A number - when multiplied by itself - is equal to a given number.
base
square root
2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten