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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. When an exponent occurs - it must always be written unless...
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.
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
its value is 1
what power is intended and what root is intended

2. Any number divided by itself is
Exponent
Decimal places in the factors together
number of minus signs
1

3. If an improper fraction occurs in an exponent it is customary to
vinculum
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.
keep the fraction in that form rather than express it as a mixed number
its value is 1

4. Any number divided by itself results in a _________ and has a value of 1
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.
Raising the numerator and the denominator separately to the power indicated
0 exponent
The inverse of raising a number to a power.

5. 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.
a root - the index of which is r.
merely moving the expression which contains the exponent to the other position in the fraction
The law of exponents for division may be developed from this example
Add the exponents and raise the common base to the sum of the exponents

6. 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.
the rule for fractional exponents to solve problems
A root of a number
1
A root

7. The line above the number whose root is to be found is a symbol of grouping called the
vinculum
Does not Exist
Zero occurs as an exponent
Raising the numerator and the denominator separately to the power indicated

8. Is the number of times the number itself is to be taken as a factor.
merely moving the expression which contains the exponent to the other position in the fraction
Exponent
The power
negative exponents arise

9. Depending on whether the exponent of the base is odd or even.
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 minus signs is odd or even -
its value is 1
1

10. The law of exponents for multiplication may be combined with
Does not Exist
the rule for fractional exponents to solve problems
The process of finding a root
1

11. To multiply two or more powers having the same base -
the power is positive
The operation of raising a number to a 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.
Add the exponents and raise the common base to the sum of the exponents

12. Is a special case of multiplication in which the factors are all equal.
the power is positive
the power is negative
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.
The operation of raising a number to a power

13. The number that indicates the root is called the
INDEX of the root
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.
Is equal to the number of places in the decimal multiplied by the exponent.
The number of minus signs is odd or even -

14. Notice that the sign of an exponent may be changed by
a root - the index of which is r.
A root of a number
merely moving the expression which contains the exponent to the other position in the fraction
its value is 1

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.
The process of finding a root
A root of a number
The power

16. When the exponent is even
number of minus signs
the power is positive
The law of exponents for division may be developed from this example
zero power

17. The sign of the product is determined - as in ordinary multiplication - by the
Positive
number of minus signs
the power is positive
Raising to a power

18. Positive and negative numbers belong to the class called
Real Numbers
A root
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 itself

19. To determine the number of decimal places in the root of a perfect power
Imaginary Number
Exponent
Divide the number of decimal places in the radicand by the index of the root.
The process of finding a root

20. In the answer to a problem such as 4^3 + 4^3.
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.
Zero occurs as an exponent
Is equal to the number of places in the decimal multiplied by the exponent.

21. Any number (other than zero) raised to the _____ equals 1
zero power
Decimal places in the factors together
The number of times that the number is to be taken as a factor
the rule for fractional exponents to solve problems

22. The power of a product is equal to the product obtained when
Add the exponents and raise the common base to the sum of the exponents
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Exponent
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.

23. The law of exponents for multiplication may be stated as follows:
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.
1
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 number itself

24. Mark off as many decimal places in the product as there are
Decimal places in the factors together
keep the fraction in that form rather than express it as a mixed number
The number itself
number of minus signs

25. It is important to realize that the base must be the same for each factor - in order to apply
A root
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.
A root of a number
The laws of exponents

26. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
vinculum
Decimal places in the factors together
keep the fraction in that form rather than express it as a mixed number
negative exponents arise

27. Is a special factor of a number.
The operation of raising a number to a power
A root
its value is 1
Raising the numerator and the denominator separately to the power indicated

28. The first power of any number is
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 laws of exponents
The number itself
The number of times that the number is to be taken as a factor

29. A fractional exponent of the form 1/r indicates
a root - the index of which is r.
The number itself
Is equal to the number of places in the decimal multiplied by the exponent.
the rule for fractional exponents to solve problems

30. 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.
Real Numbers
1
vinculum

31. When a decimal is raised to a power - the number of decimal places in the result
Is equal to the number of places in the decimal multiplied by the exponent.
INDEX of the root
The law of exponents for division may be developed from this example
Zero occurs as an exponent

32. The indicated square root of a negative number is called an
Raising to a power
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
Imaginary Number

33. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
its value is 1
Raising to a power
When the radical symbol is used
The process of taking a root of a number

34. In fraction form an exponent shows immediately
what power is intended and what root is intended
One desired
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.

35. The law of exponents for the power of a product is as follows:
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.
Real Numbers
negative exponents arise
The laws of exponents

36. The laws of exponents for the power of a power may be stated as follows:
The law of exponents for division may be developed from this example
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 process of taking a root of a number
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.

37. We recall that the exponent of a number tells
The number of times that the number is to be taken as a factor
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.
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

38. 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
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Positive
The law of exponents for division

39. When the exponent of a negative number is odd -
the power is negative
Add the exponents and raise the common base to the sum of the exponents
number of minus signs
The law of exponents for division

40. The square of a real number is
Positive
One desired
When the radical symbol is used
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

41. Finding a root of a number is
The inverse of raising a number to a power.
A root
Raising the numerator and the denominator separately to the power indicated
vinculum

42. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
A root
The number of times that the number is to be taken as a factor
Does not Exist
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.

43. 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.
The inverse of raising a number to a power.
the rule for fractional exponents to solve problems
The process of taking a root of a number
the power is negative

44. A fraction is raised to a power by
The process of finding a root
Raising the numerator and the denominator separately to the power indicated
The process of taking a root of a number
Raising to a power

45. Is multiplication in which all the numbers being multiplied together are equal.
Decimal places in the factors together
Raising to a power
Does not Exist
The operation of raising a number to a power

46. 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.
Zero occurs as an exponent
The law of exponents for division
The law of exponents for division may be developed from this example
The process of finding a root

47. The law of exponents for a power of an indicated quotient
0 exponent
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.
Exponent
A root of a number

48. When a radical has no index - the square root is understood to be the
Divide the number of decimal places in the radicand by the index of the root.
the rule for fractional exponents to solve problems
zero power
One desired

49. Is the inverse of raising a number to a power.
INDEX of the root
The process of finding a root
One desired
A root of a number