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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. 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
Is equal to the number of places in the decimal multiplied by the exponent.
A root
Raising the numerator and the denominator separately to the power indicated

2. In the answer to a problem such as 4^3 + 4^3.
what power is intended and what root is intended
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.
Zero occurs as an exponent

3. We recall that the exponent of a number tells
Real Numbers
The number of times that the number is to be taken as a factor
negative exponents arise
Exponent

4. Any number (other than zero) raised to the _____ equals 1
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.
zero power
Decimal places in the factors together

5. A fractional exponent of the form 1/r indicates
INDEX of the root
Is equal to the number of places in the decimal multiplied by the exponent.
zero power
a root - the index of which is r.

6. 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
Does not Exist
The power
The law of exponents for division

7. The law of exponents for multiplication may be combined with
the rule for fractional exponents to solve problems
The process of taking a root of a number
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.

8. When a decimal is raised to a power - the number of decimal places in the result
Raising to a power
The law of exponents for division
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

9. Is the number of times the number itself is to be taken as a factor.
A root of a number
The power
number of minus signs
a root - the index of which is r.

10. The power of a product is equal to the product obtained when
The process of finding a root
Decimal places in the factors together
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Positive

11. The law of exponents for multiplication may be stated 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.
Raising to a power
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 inverse of raising a number to a power.

12. 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 process of taking a root of a number
The process of finding a root
1
The law of exponents for division

13. The sign of the product is determined - as in ordinary multiplication - by the
merely moving the expression which contains the exponent to the other position in the fraction
The process of taking a root of a number
Divide the number of decimal places in the radicand by the index of the root.
number of minus signs

14. Is multiplication in which all the numbers being multiplied together are equal.
Raising to a power
the power is positive
INDEX of the root
keep the fraction in that form rather than express it as a mixed number

15. In fraction form an exponent shows immediately
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 of a number
a root - the index of which is r.
what power is intended and what root is intended

16. Any number divided by itself is
A root of a number
1
The number of minus signs is odd or even -
Raising the numerator and the denominator separately to the power indicated

17. When an exponent occurs - it must always be written unless...
its value is 1
When the radical symbol is used
The law of exponents for division
vinculum

18. Mark off as many decimal places in the product as there are
The process of taking a root of a number
The power
One desired
Decimal places in the factors together

19. Notice that the sign of an exponent may be changed by
The number itself
Decimal places in the factors together
merely moving the expression which contains the exponent to the other position in the fraction
its value is 1

20. The law of exponents for a power of an indicated quotient
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.
Divide the number of decimal places in the radicand by the index of the root.
The laws of exponents
A root of a number

21. Is a special case of multiplication in which the factors are all equal.
The operation of raising a number to a power
Is equal to the number of places in the decimal multiplied by the exponent.
Raising the numerator and the denominator separately to the power indicated
When the radical symbol is used

22. When a radical has no index - the square root is understood to be the
When the radical symbol is used
The inverse of raising a number to a power.
One desired
A root of a number

23. The first power of any number is
INDEX of the root
The number of times that the number is to be taken as a factor
The number itself
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.

24. Depending on whether the exponent of the base is odd or even.
The inverse 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 number of minus signs is odd or even -
1

25. Positive and negative numbers belong to the class called
Raising the numerator and the denominator separately to the power indicated
A root
Real Numbers
The operation of raising a number to a power

26. To multiply two or more powers having the same base -
The power
Add the exponents and raise the common base to the sum of the exponents
vinculum
INDEX of the root

27. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
The laws of 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.
the power is negative
the rule for fractional exponents to solve problems

28. The indicated square root of a negative number is called an
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Imaginary Number
zero power
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

29. To determine the number of decimal places in the root of a perfect power
Real Numbers
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.
Divide the number of decimal places in the radicand by the index of the root.

30. Any number divided by itself results in a _________ and has a value of 1
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.
0 exponent
negative exponents arise
Raising the numerator and the denominator separately to the power indicated

31. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
The process of taking a root of a number
A root
Does not Exist
merely moving the expression which contains the exponent to the other position in the fraction

32. The law of exponents for the power of a product is as follows:
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 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.

33. When the exponent of a negative number is odd -
the power is negative
A root of a number
0 exponent
INDEX of the root

34. Is the inverse of raising a number to a power.
The laws of exponents
The power
merely moving the expression which contains the exponent to the other position in the fraction
The process of finding a root

35. To divide one power into another having the same base
Is equal to the number of places in the decimal multiplied by the 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.
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.
Does not Exist

36. A fraction is raised to a power by
Does not Exist
Imaginary Number
Raising the numerator and the denominator separately to the power indicated
The number of times that the number is to be taken as a factor

37. 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
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.
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.

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

39. If an improper fraction occurs in an exponent it is customary to
Positive
Raising to a power
keep the fraction in that form rather than express it as a mixed number
One desired

40. 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
Is equal to the number of places in the decimal multiplied by the exponent.
number of minus signs

41. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
Raising to a power
Decimal places in the factors together
negative exponents arise
Positive

42. 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 process of finding a root
A root of a number
The power
The number of minus signs is odd or even -

43. The line above the number whose root is to be found is a symbol of grouping called the
A root of a number
what power is intended and what root is intended
The number itself
vinculum

44. The square of a real 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.
Positive
The law of exponents for division
The number itself

45. Is a special factor of a number.
A root
the power is positive
The law of exponents for division may be developed from this example
Is equal to the number of places in the decimal multiplied by the exponent.

46. It is important to realize that the base must be the same for each factor - in order to apply
A root
Zero occurs as an exponent
Raising to a power
The laws of exponents

47. Finding a root of a number is
The inverse of raising a number to a power.
A root
Divide the number of decimal places in the radicand by the index of the 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.

48. When the exponent is even
the power is positive
the power is negative
merely moving the expression which contains the exponent to the other position in the fraction
Does not Exist

49. The laws of exponents for the power of a power may be stated as follows:
The number of times that the number is to be taken as a factor
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 process of finding a root
Raising the numerator and the denominator separately to the power indicated