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CLEP General Mathematics: Exponents And Radicals

Subjects : clep, math

Instructions:

Answer 49 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 first power of any number is
its value is 1
The number itself
One desired
negative exponents arise

2. When a radical has no index - the square root is understood to be the
One desired
0 exponent
the power is positive
The number itself

3. When a decimal is raised to a power - the number of decimal places in the result
The laws of exponents
Raising to a power
Imaginary Number
Is equal to the number of places in the decimal multiplied by the exponent.

4. The law of exponents for multiplication may be stated as follows:
keep the fraction in that form rather than express it as a mixed number
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
A root
Raising the numerator and the denominator separately to the power indicated

5. To divide one power into another having the same base
Real Numbers
The law of exponents for division
Subtract the exponent of the divisor from the exponent of the dividend. Use the number resulting from this subtraction as the exponent of the base in the quotient.
0 exponent

6. Is the number of times the number itself is to be taken as a factor.
a root - the index of which is r.
negative exponents arise
The power
When the radical symbol is used

7. Positive and negative numbers belong to the class called
The number itself
1
Real Numbers
what power is intended and what root is intended

8. The law of exponents for multiplication may be combined with
the rule for fractional exponents to solve problems
The process of finding a root
negative exponents arise
Raising the numerator and the denominator separately to the power indicated

9. The law of exponents for a power of an indicated quotient
the power is negative
A root of a number
The power of a quotient is equal to the quotient obtained when the dividend and divisor are each raised to the indicated power separately - before the division is performed.
The number itself

10. Depending on whether the exponent of the base is odd or even.
keep the fraction in that form rather than express it as a mixed number
Raising to a power
The laws of exponents
The number of minus signs is odd or even -

11. Is a special factor of a number.
A root
0 exponent
The power
The law of exponents for division may be developed from this example

12. When an exponent occurs - it must always be written unless...
0 exponent
its value is 1
The operation of raising a number to a power
The process of taking a root of a number

13. The inverse of the process of raising the number to a power - and the method of taking the root of a fraction is similar. We may simply take the root of each term separately and write the result as a fraction.
Is equal to the number of places in the decimal multiplied by the exponent.
The law of exponents for division may be developed from this example
The process of taking a root of a number
keep the fraction in that form rather than express it as a mixed number

14. The line above the number whose root is to be found is a symbol of grouping called the
Real Numbers
The operation of raising a number to a power
vinculum
a root - the index of which is r.

15. To divide one power into another having the same base - subtract the exponent of the divisor from the exponent of the dividend. Use the number resulting from this subtraction as the exponent of the base in the quotient.
Add the exponents and raise the common base to the sum of the exponents
The law of exponents for division
merely moving the expression which contains the exponent to the other position in the fraction
A root of a number

16. To multiply two or more powers having the same base -
negative exponents arise
A root
Add the exponents and raise the common base to the sum of the exponents
zero power

17. When the exponent is even
Imaginary Number
Its numerator is 1; its denominator is N with a positive exponent whose absolute value is the same as the absolute value of the original exponent.
the power is positive
number of minus signs

18. In fraction form an exponent shows immediately
what power is intended and what root is intended
Subtract the exponent of the divisor from the exponent of the dividend. Use the number resulting from this subtraction as the exponent of the base in the quotient.
Zero occurs as an exponent
When the radical symbol is used

19. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
Its numerator is 1; its denominator is N with a positive exponent whose absolute value is the same as the absolute value of the original exponent.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Is equal to the number of places in the decimal multiplied by the exponent.
Imaginary Number

20. A fraction is raised to a power by
Raising to a power
Exponent
merely moving the expression which contains the exponent to the other position in the fraction
Raising the numerator and the denominator separately to the power indicated

21. A power of a number is indicated by an___ - which is a number in small print placed to the right and toward the top of the number.
Exponent
vinculum
Subtract the exponent of the divisor from the exponent of the dividend. Use the number resulting from this subtraction as the exponent of the base in the quotient.
The number of times that the number is to be taken as a factor

22. It is important to realize that the base must be the same for each factor - in order to apply
The number of times that the number is to be taken as a factor
The law of exponents for division may be developed from this example
The laws of exponents
its value is 1

23. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
Add the exponents and raise the common base to the sum of the exponents
Real Numbers
negative exponents arise
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

24. The sign of the product is determined - as in ordinary multiplication - by the
Imaginary Number
The process of finding a root
number of minus signs
Raising the numerator and the denominator separately to the power indicated

25. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
When the radical symbol is used
The power
number of minus signs
the rule for fractional exponents to solve problems

26. Is a special case of multiplication in which the factors are all equal.
Zero occurs as an exponent
the power is negative
The operation of raising a number to a power
0 exponent

27. Cancellation of the five 6's in the divisor with five of the 6 's in the dividend leaves only two 6's - the product of which is 6^2.
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
The law of exponents for division may be developed from this example
Positive
Raising the numerator and the denominator separately to the power indicated

28. In the answer to a problem such as 4^3 + 4^3.
the power is positive
Add the exponents and raise the common base to the sum of the exponents
The process of taking a root of a number
Zero occurs as an exponent

29. A fractional exponent of the form 1/r indicates
The number itself
a root - the index of which is r.
The law of exponents for division may be developed from this example
Positive

30. When the exponent of a negative number is odd -
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
The process of finding a root
the power is negative
Decimal places in the factors together

31. The laws of exponents for the power of a power may be stated as follows:
what power is intended and what root is intended
The law of exponents for division may be developed from this example
Real Numbers
To find the power of a power - multiply the exponents. It should be noted that this case is the only one in which multiplication of exponents is performed.

32. If an improper fraction occurs in an exponent it is customary to
keep the fraction in that form rather than express it as a mixed number
Raising to a power
INDEX of the root
Does not Exist

33. Mark off as many decimal places in the product as there are
A root of a number
Decimal places in the factors together
The process of taking a root of a number
Its numerator is 1; its denominator is N with a positive exponent whose absolute value is the same as the absolute value of the original exponent.

34. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
the power is positive
keep the fraction in that form rather than express it as a mixed number
Does not Exist

35. The number that indicates the root is called the
INDEX of the root
A root of a number
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
To find the power of a power - multiply the exponents. It should be noted that this case is the only one in which multiplication of exponents is performed.

36. The indicated square root of a negative number is called an
The law of exponents for division
what power is intended and what root is intended
Imaginary Number
zero power

37. We recall that the exponent of a number tells
To find the power of a power - multiply the exponents. It should be noted that this case is the only one in which multiplication of exponents is performed.
Divide the number of decimal places in the radicand by the index of the root.
The number of times that the number is to be taken as a factor
vinculum

38. Any number divided by itself is
1
Is equal to the number of places in the decimal multiplied by the exponent.
When the radical symbol is used
what power is intended and what root is intended

39. The law of exponents for the power of a product is as follows:
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
To find the power of a power - multiply the exponents. It should be noted that this case is the only one in which multiplication of exponents is performed.
zero power
The power of a product is equal to the product obtained when each of the original factors is raised to the indicated power and the resulting powers are multiplied together.

40. Any number (other than zero) raised to the _____ equals 1
zero power
The process of taking a root of a number
Add the exponents and raise the common base to the sum of the exponents
The power of a product is equal to the product obtained when each of the original factors is raised to the indicated power and the resulting powers are multiplied together.

41. To determine the number of decimal places in the root of a perfect power
what power is intended and what root is intended
Divide the number of decimal places in the radicand by the index of the root.
The operation of raising a number to a power
The law of exponents for division

42. Any number divided by itself results in a _________ and has a value of 1
The operation of raising a number to a power
To find the power of a power - multiply the exponents. It should be noted that this case is the only one in which multiplication of exponents is performed.
0 exponent
Does not Exist

43. Notice that the sign of an exponent may be changed by
merely moving the expression which contains the exponent to the other position in the fraction
Its numerator is 1; its denominator is N with a positive exponent whose absolute value is the same as the absolute value of the original exponent.
Divide the number of decimal places in the radicand by the index of the root.
the power is negative

44. The square of a real number is
merely moving the expression which contains the exponent to the other position in the fraction
Positive
The number itself
A root of a number

45. Can be indicated by placing a radical sign - ..r - over the number and showing the root by placing a small number within the notch of the radical sign.
Exponent
The law of exponents for division
The law of exponents for division may be developed from this example
A root of a number

46. Is multiplication in which all the numbers being multiplied together are equal.
Raising to a power
Does not Exist
Zero occurs as an exponent
Raising the numerator and the denominator separately to the power indicated

47. The power of a product is equal to the product obtained when
The operation of raising a number to a power
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
The law of exponents for division may be developed from this example
A root of a number

48. Finding a root of a number is
The inverse of raising a number to a power.
Its numerator is 1; its denominator is N with a positive exponent whose absolute value is the same as the absolute value of the original exponent.
what power is intended and what root is intended
Exponent

49. Is the inverse of raising a number to a power.
Zero occurs as an exponent
The operation of raising a number to a power
The process of finding a root
The number of minus signs is odd or even -