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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. The cube root of zero is
radical sign
0
negative number
itself

2. 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.
cube root
base
Scientific notation
10^1

3. Any number with an exponent of 1 is equal to
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.
you have to adjust the value of the exponent in order avoid changing the actual value.
itself
1

4. 1^4 =
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1
Engineering notation
2 x 10^9

5. Dividing by 10
rewrite one of the terms so that the exponents are equal
Moving the decimal point to the left
10^-2
same exponent

6. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
coefficient
2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1

7. A number is a second number which - when multiplied by itself three times - equals the original number.
0
1
perfect square
cube root

8. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Calculator square-root key
Because 4 multiplied by itself equals 16.
cubed

9. 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
1. Divide the coefficients 2. Subtract the exponents
adjust the value of the coefficient
2

10. When you move the decimal point in the coefficient to the right
Same base
cube-root key
1 divided by that number with a positive exponent
decrease the power-of-10 exponent by the same number of units

11. To multiply or divide exponent terms that do not have the same base:
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
exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

12. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
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
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

13. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
Subtract the exponent
Because 4 multiplied by itself equals 16.
Same base

14. The square root of zero is
move the decimal point the same number of units to the left
change both terms in order to keep the value the same.
a fractional decimal
0

15. The decimal part
2
base
square root
coefficient

16. 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.
Not
rewrite one of the terms so that the exponents are equal
0

17. 10 - or 1 with the decimal point moved one place 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
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^1
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. The symbol for the cube root of a number is
1
the radical sign with a little 3 that indicates the cube root:
1. Divide the coefficients 2. Subtract the exponents
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

19. There are no special rules for adding and subtracting numbers that are written with exponents.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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
5
10^-1

20. Indicates the number to be multiplied.
base
10^-18
cubed
Step 1. Divide the coefficients of the terms

21. 1 to any power is equal to
1
move the decimal point the same number of units to the left
cube root
When the exponent of a power-of-10 expression is a negative integer:

22. 5^1 =
5
negative number
must be multiples of 3 or 0
Subtract the exponent

23. The cube root of a negative number is also a
negative number
same exponent
increase the power-of-10 exponent by the same number of units
2 x 10^9

24. For the 10
exponent
increase the power-of-10 exponent by the same number of units
0
coefficient

25. When you move the decimal point in the coefficient to the left
move the decimal point the same number of units to the right
When the exponent of a power-of-10 expression is a negative integer:
proper scientific
increase the power-of-10 exponent by the same number of units

26. 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
2
one digit to the left of the decimal point
Calculator square-root key

27. To multiply powers of ten:
perfect square
10^2
1. Multiply the coefficients 2. Add the exponents
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

28. What number multiplied by itself is equal to 16? The answer is 4. Why?
same exponent
10^-18
Because 4 multiplied by itself equals 16.
When the exponent of a power-of-10 expression is a negative integer:

29. 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
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
same exponent
change both terms in order to keep the value the same.
Subtract the exponent

30. Any number with an exponent of 0 is equal to
itself
10^-18
1
base

31. To divide powers of 10:
base
Step 1. Divide the coefficients of the terms
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
proper scientific

32. 0^5 =
When the exponent of a power-of-10 expression is a negative integer:
0
proper scientific
must be multiples of 3 or 0

33.
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
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
When moving the decimal point to the left (dividing by 10)

34. A very small number such as 0.000000674 can be written with scientific notation as
base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
square root
6.74 x 10^-7

35. Don't bother trying to find the square root of a negative number.
10^2
The solution exists - but not in the real number system.
the radical sign with a little 3 that indicates the cube root:
1

36. When you decrease the value of the power-of-10 exponent
10^1
move the decimal point the same number of units to the right
1
Moving the decimal point to the right

37. = 0.1 - or 1 with the decimal point moved one place to the left.
1
10^-1
exponent
0

38. 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
exponent
move the decimal point the same number of units to the left
Subtract the exponent

39. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
negative number
1. Multiply the coefficients 2. Add the exponents
itself

40. 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.
To multiply powers that have the same base:
the radical sign with a little 3 that indicates the cube root:
10^-1

41. Increase the value of the exponent by 1 (multiplying by 10)
Moving the decimal point to the left
decrease the power-of-10 exponent by the same number of units
1 divided by that number with a positive exponent
When moving the decimal point to the left (dividing by 10)

42. 3^0 =
decrease the power-of-10 exponent by the same number of units
Subtract the exponent
2 x 10^9
1

43. Always 10 for scientific notation
0
The solution exists - but not in the real number system.
base
cube-root key

44. Negative cube roots are okay ... negative square roots are
Not
1. Divide the coefficients 2. Subtract the exponents
perfect square
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

45. A number with an exponent of 3 is often said to be
10^-18
10^-2
1. Multiply the coefficients 2. Add the exponents
cubed

46. Scientific notation requires there to be only
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^-18
one digit to the left of the decimal point
Calculator square-root key

47. 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.
0
Moving the decimal point to the right
radical sign
10^-2

48. = 0.01 - or 1 with the decimal point moved two places to the left.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
base
10^-2
Moving the decimal point to the right

49. To divide powers of ten:
must be multiples of 3 or 0
1. Divide the coefficients 2. Subtract the exponents
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

50. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
move the decimal point the same number of units to the left
cubed
2 x 10^9
Calculator square-root key