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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. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
move the decimal point the same number of units to the right
3
10^-1

2. Numbers with exponents can be directly multiplied or divided only when they have the
coefficient
you have to adjust the value of the exponent in order avoid changing the actual value.
Not
Same base

3. A number with an exponent of 3 is often said to be
Engineering notation
Step 1. Divide the coefficients of the terms
2
cubed

4. Indicates the number to be multiplied.
Step 1. Divide the coefficients of the terms
base
9 (3^2 = 9)
0

5. The decimal part
1
coefficient
Moving the decimal point to the left
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

6.
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
exponent
0

7. Step 1: Add the exponents Step 2: Use the common base
squared
10^-2
itself
To multiply powers that have the same base:

8. Scientific notation requires there to be only
Not
square root
one digit to the left of the decimal point
Are Equal

9. A very small number such as 0.000000674 can be written with scientific notation as
decrease the value of the exponent by 1 (dividing by 10)
10^2
10^-18
6.74 x 10^-7

10. There are no special rules for adding and subtracting numbers that are written with exponents.
1. Divide the coefficients 2. Subtract the exponents
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
must be multiples of 3 or 0
Because 4 multiplied by itself equals 16.

11. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
decrease the value of the exponent by 1 (dividing by 10)
cubed
cube-root key

12. To divide powers of 10:
1. Multiply the coefficients 2. Add the exponents
Step 1. Divide the coefficients of the terms
increase the power-of-10 exponent by the same number of units
cube root

13. Always 10 for scientific notation
base
0
same exponent
adjust the value of the coefficient

14. 0^5 =
cube-root key
The solution exists - but not in the real number system.
0
square root

15. 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
move the decimal point the same number of units to the right
one digit to the left of the decimal point
1. Divide the coefficients 2. Subtract the exponents

16. When the exponents are not the same
cube root
1 divided by that number with a positive exponent
rewrite one of the terms so that the exponents are equal
Moving the decimal point to the left

17. Valid powers-of-10 for engineering notation
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
negative number
must be multiples of 3 or 0
1

18. To find the square root of any number - simply key in the number (the radicand) and press the
0
Calculator square-root key
10^1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

19. 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
10^1
change both terms in order to keep the value the same.
Same base
Are Equal

20. 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
5
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)

21. 5^1 =
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^1
When the exponent of a power-of-10 expression is a negative integer:
5

22. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
itself
2
1. Divide the coefficients 2. Subtract the exponents
0

23. 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
Same base
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)
radical sign

24. To divide powers of ten:
increase the power-of-10 exponent by the same number of units
1. Divide the coefficients 2. Subtract the exponents
rewrite one of the terms so that the exponents are equal
perfect square

25. 3^0 =
move the decimal point the same number of units to the left
0
decrease the power-of-10 exponent by the same number of units
1

26. 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.
Are Equal
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Scientific notation
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

27. To multiply powers of ten:
rewrite one of the terms so that the exponents are equal
1. Multiply the coefficients 2. Add the exponents
6.74 x 10^-7
5

28. When moving the decimal point to the right (multiplying by 10)
6.74 x 10^-7
Because 4 multiplied by itself equals 16.
decrease the value of the exponent by 1 (dividing by 10)
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

29. 0 to any power is equal to
0
cube root
cubed
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

30. When you change the position of the decimal point in a coefficient value
1
you have to adjust the value of the exponent in order avoid changing the actual value.
cube-root key
1. Divide the coefficients 2. Subtract the exponents

31. Any number with an exponent of 1 is equal to
exponent
cubed
itself
a fractional decimal

32. Indicates the number of times the base is to be multiplied.
exponent
1
decrease the value of the exponent by 1 (dividing by 10)
adjust the value of the coefficient

33. Any number with a negative exponent is equal to
When moving the decimal point to the left (dividing by 10)
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0
1 divided by that number with a positive exponent

34. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
exponent
9 (3^2 = 9)
Not

35. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
2 x 10^9
exponent
10^2

36. Don't bother trying to find the square root of a negative number.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1. Divide the coefficients 2. Subtract the exponents
The solution exists - but not in the real number system.
one digit to the left of the decimal point

37. The cube root of a negative number is also a
coefficient
negative number
cube root
the radical sign with a little 3 that indicates the cube root:

38. To multiply powers of 10:
the radical sign with a little 3 that indicates the cube root:
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.
perfect square

39. The square root of 9 is
move the decimal point the same number of units to the right
10^1
3
must be multiples of 3 or 0

40. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
1. Divide the coefficients 2. Subtract the exponents
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
6.74 x 10^-7

41. 100 - or 1 with the decimal point moved two places to the right
exponent
cubed
10^2
The solution exists - but not in the real number system.

42. 1 to any power is equal to
The solution exists - but not in the real number system.
10^-1
6.74 x 10^-7
1

43. 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
1
move the decimal point the same number of units to the left
change both terms in order to keep the value the same.

44. 1 to any power is equal to
move the decimal point the same number of units to the left
increase the power-of-10 exponent by the same number of units
3
1

45. For the 10
10^1
exponent
rewrite one of the terms so that the exponents are equal
1

46. A number is a second number which - when multiplied by itself three times - equals the original number.
The solution exists - but not in the real number system.
cube root
Subtract the exponent
1

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
0
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
2 x 10^9

48. 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.
base
When the exponent of a power-of-10 expression is a negative integer:
3
0

49. 10 - or 1 with the decimal point moved one place to the right
decrease the value of the exponent by 1 (dividing by 10)
To multiply powers that have the same base:
itself
10^1

50. = 0.01 - or 1 with the decimal point moved two places to the left.
1
0
itself
10^-2

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CLEP General Mathematics: Powers Exponents And Roots

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