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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. 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.
9 (3^2 = 9)
Engineering notation
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

2. What number multiplied by itself is equal to 16? The answer is 4. Why?
Same base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Because 4 multiplied by itself equals 16.
5

3. 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.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
2 x 10^9
Scientific notation
2

4. Negative cube roots are okay ... negative square roots are
cube root
1. Divide the coefficients 2. Subtract the exponents
0
Not

5. A negative exponent does not mean the decimal value is negative. It means the decimal value is
exponent
Engineering notation
a fractional decimal
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

6. When you change the position of the decimal point in a coefficient value
exponent
you have to adjust the value of the exponent in order avoid changing the actual value.
move the decimal point the same number of units to the left
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.

7. To multiply powers of 10:
10^-2
Same base
1 divided by that number with a positive 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.

8. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
radical sign
base
you have to adjust the value of the exponent in order avoid changing the actual value.

9. The square root of zero is
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.
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
0
itself

10. Dividing by 10
itself
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
cube root
Moving the decimal point to the left

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
To multiply powers that have the same base:
5
must be multiples of 3 or 0

12. 1^4 =
0
proper scientific
a fractional decimal
1

13. A number - when multiplied by itself - is equal to a given number.
one digit to the left of the decimal point
Subtract the exponent
base
square root

14. Any number with an exponent of 0 is equal to
Scientific 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
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

15. 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.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Same base
When the exponent of a power-of-10 expression is a negative integer:
1. Divide the coefficients 2. Subtract the exponents

16. A number with an exponent of 2 is often said to be
squared
itself
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

17. 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.
2
10^-2
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

18. To multiply or divide exponent terms that do not have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
cubed
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)

19. Any number with a negative exponent is equal to
1
1 divided by that number with a positive exponent
perfect square
base

20. To subtract powers of ten:
decrease the power-of-10 exponent by the same number of units
move the decimal point the same number of units to the right
Calculator square-root key
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

21. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
decrease the power-of-10 exponent by the same number of units
2
squared
Are Equal

22. Multiplying by 10
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the right
Not
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

23. For the 10
5
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
exponent
the radical sign with a little 3 that indicates the cube root:

24. 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
To multiply powers that have the same base:
6.74 x 10^-7
1 divided by that number with a positive exponent

25. A very small number such as 0.000000674 can be written with scientific notation as
10^-2
10^-1
change both terms in order to keep the value the same.
6.74 x 10^-7

26. To add powers of ten:
2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1
exponent

27. When the exponents are not the same
rewrite one of the terms so that the exponents 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
Not
1

28. 100 - or 1 with the decimal point moved two places to the right
1
10^2
6.74 x 10^-7
squared

29. The decimal part
coefficient
you have to adjust the value of the exponent in order avoid changing the actual value.
To multiply powers that have the same base:
increase the power-of-10 exponent by the same number of units

30. Numbers with exponents can be directly multiplied or divided only when they have the
Moving the decimal point to the left
1
Same base
Not

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.
Engineering notation
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
perfect square
1

32. 3^0 =
move the decimal point the same number of units to the left
1
adjust the value of the coefficient
cube root

33. = 0.01 - or 1 with the decimal point moved two places to the left.
Subtract the exponent
1
10^-2
radical sign

34. A number with an exponent of 3 is often said to be
cubed
decrease the value of the exponent by 1 (dividing by 10)
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
rewrite one of the terms so that the exponents are equal

35. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1
base
the radical sign with a little 3 that indicates the cube root:

36. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
square root
exponent
2 x 10^9
base

37. When you move the decimal point in the coefficient to the left
one digit to the left of the decimal point
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
0
increase the power-of-10 exponent by the same number of units

38. When you decrease the value of the power-of-10 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
move the decimal point the same number of units to the right
Moving the decimal point to the right
Same base

39. Indicates the number of times the base is to be multiplied.
cubed
one digit to the left of the decimal point
exponent
Scientific notation

40. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Not
Subtract the exponent
Same base
2

41. Powers of ten can be added or subtracted only when their exponents
Are Equal
square root
1
move the decimal point the same number of units to the left

42. 0^5 =
1
1
0
The solution exists - but not in the real number system.

43. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
10^-2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power 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.

44. When moving the decimal point to the right (multiplying by 10)
When the exponent of a power-of-10 expression is a negative integer:
decrease the value of the exponent by 1 (dividing by 10)
Engineering notation
Are Equal

45. Valid powers-of-10 for engineering notation
Step 1. Divide the coefficients of the terms
must be multiples of 3 or 0
Moving the decimal point to the right
decrease the value of the exponent by 1 (dividing by 10)

46. The symbol for the cube root of a number is
0
the radical sign with a little 3 that indicates the cube root:
base
itself

47. 0 to any power is equal to
0
Moving the decimal point to the right
a fractional decimal
Not

48. Scientific notation requires there to be only
square root
1
one digit to the left of the decimal point
9 (3^2 = 9)

49. 5^1 =
0
one digit to the left of the decimal point
5
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

50.
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. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
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