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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. 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
10^1
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
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

2. Indicates the number of times the base is to be multiplied.
exponent
rewrite one of the terms so that the exponents are equal
10^1
adjust the value of the coefficient

3. 1 to any power is equal to
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
radical sign
Same base

4. 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.
decrease the value of the exponent by 1 (dividing by 10)
Are Equal
3
perfect square

5. 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.
decrease the power-of-10 exponent by the same number of units
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
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

6. The square of 3 is
one digit to the left of the decimal point
itself
9 (3^2 = 9)
decrease the value of the exponent by 1 (dividing by 10)

7. To add or subtract numbers written with exponents:
Subtract the exponent
adjust the value of the coefficient
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Divide the coefficients of the terms

8. 0^5 =
rewrite one of the terms so that the exponents are equal
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
2 x 10^9
0

9. To divide powers of ten:
cube-root key
square root
itself
1. Divide the coefficients 2. Subtract the exponents

10. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-18
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

11. Multiplying by 10
Moving the decimal point 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
a fractional decimal
the radical sign with a little 3 that indicates the cube root:

12. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
one digit to the left of the decimal point
decrease the value of the exponent by 1 (dividing by 10)
1. Divide the coefficients 2. Subtract the exponents

13. Indicates the number to be multiplied.
0
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
base

14. 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.
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
perfect square
Engineering notation

15. There are no special rules for adding and subtracting numbers that are written with exponents.
adjust the value of the coefficient
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^2
Are Equal

16. When you move the decimal point in the coefficient to the left
0
Calculator square-root key
increase the power-of-10 exponent by the same number of units
negative number

17. Valid powers of 10 for engineering notation are:
square root
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
adjust the value of the coefficient
9 (3^2 = 9)

18. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
0
move the decimal point the same number of units to the right
must be multiples of 3 or 0

19. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
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.
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

20. To divide powers of 10:
Step 1. Divide the coefficients of the terms
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
you have to adjust the value of the exponent in order avoid changing the actual value.
Are Equal

21. 100 - or 1 with the decimal point moved two places to the right
10^2
itself
perfect square
1 divided by that number with a positive exponent

22. A very small number such as 0.000000674 can be written with scientific notation as
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
square root
6.74 x 10^-7
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

23. Adding and subtracting powers of ten can be a bit more complicated than multiplying and dividing. The main problem is that powers of ten can be added or subtracted only when both terms have the
same exponent
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.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

24. The cube root of a negative number is also a
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
10^-1
negative number
same exponent

25. The cube root of zero is
To multiply powers that have the same base:
6.74 x 10^-7
cubed
0

26. For the 10
1 divided by that number with a positive exponent
cubed
coefficient
exponent

27. When moving the decimal point to the right (multiplying by 10)
Not
decrease the value of the exponent by 1 (dividing by 10)
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.

28. 3^0 =
adjust the value of the coefficient
Same base
0
1

29. 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
Moving the decimal point to the right
2 x 10^9
change both terms in order to keep the value the same.

30. To subtract powers of ten:
Moving the decimal point to the left
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Engineering notation
a fractional decimal

31. 5^1 =
0
itself
5
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

32. The square root of 9 is
1
3
base
exponent

33. A number with an exponent of 3 is often said to be
1 divided by that number with a positive exponent
Subtract the exponent
cubed
0

34. Don't bother trying to find the square root of a negative number.
1
radical sign
The solution exists - but not in the real number system.
2

35. When you move the decimal point in the coefficient to the right
increase the power-of-10 exponent by the same number of units
decrease the power-of-10 exponent by the same number of units
cube root
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

36. 0 to any power is equal to
Are Equal
To multiply powers that have the same base:
0
10^2

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.
Are Equal
Moving the decimal point to the left
When the exponent of a power-of-10 expression is a negative integer:
Engineering notation

38. A number with an exponent of 2 is often said to be
squared
decrease the power-of-10 exponent by the same number of units
proper scientific
10^-1

39. = 0.01 - or 1 with the decimal point moved two places to the left.
When the exponent of a power-of-10 expression is a negative integer:
10^-2
1
3

40. 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
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.
move the decimal point the same number of units to the right

41. Any number with an exponent of 0 is equal to
10^-18
1
move the decimal point the same number of units to the left
Engineering notation

42. Valid powers-of-10 for engineering notation
a fractional decimal
10^-2
must be multiples of 3 or 0
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. Any number with an exponent of 1 is equal to
itself
Moving the decimal point to the right
10^-1
0

44. Negative cube roots are okay ... negative square roots are
Not
Scientific notation
Calculator square-root key
negative number

45. Any number with a negative exponent is equal to
cube root
change both terms in order to keep the value the same.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1 divided by that number with a positive exponent

46. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
cubed
0
10^-1
2

47. = 0.1 - or 1 with the decimal point moved one place to the left.
same exponent
10^-1
2 x 10^9
cube root

48. Always 10 for scientific notation
proper scientific
Subtract the exponent
10^1
base

49. Scientific notation requires there to be only
6.74 x 10^-7
one digit to the left of the decimal point
the radical sign with a little 3 that indicates the cube root:
When moving the decimal point to the left (dividing by 10)

50. 1^4 =
0
1
you have to adjust the value of the exponent in order avoid changing the actual value.
Calculator square-root key