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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. Mark off as many decimal places in the product as there are
One desired
Does not Exist
Decimal places in the factors together
A root of a number

2. 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
The process of finding a root
0 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.

3. Any number divided by itself results in a _________ and has a value of 1
The number of times that the number is to be taken as a factor
0 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.
Exponent

4. The laws of exponents for the power of a power may be stated as follows:
A root of a number
Does not Exist
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.

5. We recall that the exponent of a number tells
A root
When the radical symbol is used
The number of times that the number is to be taken as a factor
The law of exponents for division

6. When the exponent of a negative number is odd -
When the radical symbol is used
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 negative
A root

7. In fraction form an exponent shows immediately
Real Numbers
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 of minus signs is odd or even -
what power is intended and what root is intended

8. It is important to realize that the base must be the same for each factor - in order to apply
its value is 1
the power is positive
The laws of 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.

9. Any number (other than zero) raised to the _____ equals 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.
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
zero power
Add the exponents and raise the common base to the sum of the exponents

10. The law of exponents for a power of an indicated quotient
One desired
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
The laws of exponents

11. In the answer to a problem such as 4^3 + 4^3.
the power is positive
The process of finding a root
One desired
Zero occurs as an exponent

12. The indicated square root of a negative number is called an
Zero occurs as an exponent
The laws of exponents
Imaginary Number
its value is 1

13. The number that indicates the root is called the
The number of minus signs is odd or even -
what power is intended and what root is intended
The process of finding a root
INDEX of the root

14. When a radical has no index - the square root is understood to be the
The law of exponents for division may be developed from this example
the power is positive
The power
One desired

15. When a decimal is raised to a power - the number of decimal places in the result
One desired
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.
The process of taking a root of a number
Is equal to the number of places in the decimal multiplied by the exponent.

16. 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
The process of finding a root
The number of minus signs is odd or even -
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.

17. Is a special factor of a number.
the rule for fractional exponents to solve problems
Exponent
A root
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

18. 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 number of minus signs is odd or even -
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
A root of a number
Does not Exist

19. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
Does not Exist
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.
1
number of minus signs

20. To divide one power into another having the same base
Imaginary Number
A root
The inverse of raising a number to a power.
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.

21. Finding a root of a number is
The laws of exponents
Real Numbers
The inverse of raising a number to a power.
1

22. A fractional exponent of the form 1/r indicates
The number of times that the number is to be taken as a factor
a root - the index of which is r.
merely moving the expression which contains the exponent to the other position in the fraction
0 exponent

23. 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.
The law of exponents for division may be developed from this example
keep the fraction in that form rather than express it as a mixed number
The process of taking a root of a number
The number of minus signs is odd or even -

24. 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.
A root of a number
merely moving the expression which contains the exponent to the other position in the fraction
The operation of raising a number to a power
Exponent

25. The law of exponents for the power of a product is as follows:
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.
what power is intended and what root is intended
Zero occurs as an exponent
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.

26. The line above the number whose root is to be found is a symbol of grouping called the
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
vinculum
what power is intended and what root is intended
the power is positive

27. Is multiplication in which all the numbers being multiplied together are equal.
Real Numbers
The process of finding a root
Raising to a power
Decimal places in the factors together

28. When an exponent occurs - it must always be written unless...
its value is 1
number of minus signs
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
Exponent

29. The law of exponents for multiplication may be combined with
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.
1
the rule for fractional exponents to solve problems
The law of exponents for division

30. 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.
Decimal places in the factors together
Raising to a power
Raising the numerator and the denominator separately to the power indicated
The law of exponents for division

31. 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
A root of a number
Divide the number of decimal places in the radicand by the index of the root.
The process of finding a root

32. To determine the number of decimal places in the root of a perfect power
Does not Exist
Real Numbers
Raising the numerator and the denominator separately to the power indicated
Divide the number of decimal places in the radicand by the index of the root.

33. Depending on whether the exponent of the base is odd or even.
what power is intended and what root is intended
the power is positive
merely moving the expression which contains the exponent to the other position in the fraction
The number of minus signs is odd or even -

34. The sign of the product is determined - as in ordinary multiplication - by the
The inverse of raising a number to a power.
The law of exponents for division
number of minus signs
The process of taking a root of a number

35. Is the inverse of raising a number to a power.
The process of finding a root
number of minus signs
the power is negative
Is equal to the number of places in the decimal multiplied by the exponent.

36. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
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 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.
its value is 1
negative exponents arise

37. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
the power is negative
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.
zero power
The inverse of raising a number to a power.

38. The first power of any number is
Raising the numerator and the denominator separately to the power indicated
a root - the index of which is r.
The laws of exponents
The number itself

39. Any number divided by itself is
what power is intended and what root is intended
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.
The law of exponents for division
1

40. 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 law of exponents for division
The process of taking a root of a number
Divide the number of decimal places in the radicand by the index of the root.
A root of a number

41. To multiply two or more powers having the same base -
Positive
number of minus signs
Add the exponents and raise the common base to the sum of the exponents
One desired

42. The square of a real number is
0 exponent
vinculum
Decimal places in the factors together
Positive

43. A fraction is raised to a power by
Zero occurs as an exponent
Raising the numerator and the denominator separately to the power indicated
0 exponent
the rule for fractional exponents to solve problems

44. Is a special case of multiplication in which the factors are all equal.
A root
One desired
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

45. When the exponent is even
Add the exponents and raise the common base to the sum of the exponents
The operation of raising a number to a power
keep the fraction in that form rather than express it as a mixed number
the power is positive

46. Positive and negative numbers belong to the class called
1
Real Numbers
The law of exponents for division
negative exponents arise

47. The power of a product is equal to the product obtained when
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 operation of raising a number to a power
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.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

48. The law of exponents for multiplication may be stated as follows:
the power is negative
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 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.
One desired

49. Is the number of times the number itself is to be taken as a factor.
A root of a number
The power
Is equal to the number of places in the decimal multiplied by the exponent.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together