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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 the exponent of a negative number is odd -
keep the fraction in that form rather than express it as a mixed number
When the radical symbol is used
the power is negative
Positive

2. When an exponent occurs - it must always be written unless...
the rule for fractional exponents to solve problems
Zero occurs as an exponent
its value is 1
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

3. The number that indicates the root is called the
The law of exponents for division
A root of a number
INDEX of the root
Real Numbers

4. The laws of exponents for the power of a power may be stated as follows:
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.
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 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.
negative exponents arise

5. When a radical has no index - the square root is understood to be the
INDEX of the root
One desired
The process of finding a root
the power is negative

6. Is a special case of multiplication in which the factors are all equal.
vinculum
the power is positive
The process of finding a root
The operation of raising a number to a power

7. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
The operation of raising a number to a power
A root of a number
Exponent
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. Depending on whether the exponent of the base is odd or even.
A root of a number
The number of minus signs is odd or even -
Divide the number of decimal places in the radicand by the index of the root.
1

9. 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
Decimal places in the factors 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.
Does not Exist

10. 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
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
The inverse of raising a number to a power.

11. The law of exponents for multiplication may be stated as follows:
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
negative exponents arise
A root of a number
When the radical symbol is used

12. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
its value is 1
Does not Exist
Raising the numerator and the denominator separately to the power indicated
merely moving the expression which contains the exponent to the other position in the fraction

13. When the exponent is even
Zero occurs as an exponent
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
The number of times that the number is to be taken as a factor

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

15. 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 power is positive
zero power
Raising the numerator and the denominator separately to the power indicated
The law of exponents for division may be developed from this example

16. The sign of the product is determined - as in ordinary multiplication - by the
Real Numbers
number of minus signs
A root
1

17. In fraction form an exponent shows immediately
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 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.
INDEX of the root
what power is intended and what root is intended

18. Is the inverse of raising a number to a power.
The process of finding a root
the power is positive
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

19. 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.
The inverse of raising a number to a power.
The number of times that the number is to be taken as a factor
the power is negative
Exponent

20. Finding a root of a number is
The power
The inverse 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.
The number of minus signs is odd or even -

21. Mark off as many decimal places in the product as there are
When the radical symbol is used
its value is 1
merely moving the expression which contains the exponent to the other position in the fraction
Decimal places in the factors together

22. In the answer to a problem such as 4^3 + 4^3.
The inverse of raising a number to a power.
The process of taking a root of a number
The number of times that the number is to be taken as a factor
Zero occurs as an exponent

23. Is a special factor 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.
A root
Real Numbers
The inverse of raising a number to a power.

24. Is multiplication in which all the numbers being multiplied together are equal.
Raising to a power
A root
Is equal to the number of places in the decimal multiplied by the exponent.
Add the exponents and raise the common base to the sum of the exponents

25. The indicated square root of a negative number is called an
a root - the index of which is r.
The number of times that the number is to be taken as a factor
Imaginary Number
negative exponents arise

26. A fractional exponent of the form 1/r indicates
a root - the index of which is r.
The process of finding a root
Add the exponents and raise the common base to the sum of the exponents
Is equal to the number of places in the decimal multiplied by the exponent.

27. Any number divided by itself is
merely moving the expression which contains the exponent to the other position in the fraction
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.
Decimal places in the factors together

28. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
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.
When the radical symbol is used
negative exponents arise
Zero occurs as an exponent

29. The power of a product is equal to the product obtained when
0 exponent
its value is 1
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
INDEX of the root

30. Any number (other than zero) raised to the _____ equals 1
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
0 exponent
The inverse of raising a number to a power.
zero power

31. 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 operation of raising a number to a power
Does not Exist
The process of taking a root of a number
The laws of exponents

32. 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.
A root of a number
1
Decimal places in the factors together
0 exponent

33. When a decimal is raised to a power - the number of decimal places in the result
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.
Is equal to the number of places in the decimal multiplied by the exponent.
Add the exponents and raise the common base to the sum of the exponents
Zero occurs as an exponent

34. It is important to realize that the base must be the same for each factor - in order to apply
Zero occurs as an exponent
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
A root of a number
The laws of exponents

35. The first power of any number is
Raising the numerator and the denominator separately to the power indicated
what power is intended and what root is intended
The number itself
Exponent

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

37. To multiply two or more powers having the same base -
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
Add the exponents and raise the common base to the sum of the exponents
Raising to a power

38. Positive and negative numbers belong to the class called
Real Numbers
The number itself
Decimal places in the factors together
Raising the numerator and the denominator separately to the power indicated

39. The law of exponents for the power of a product is as follows:
Raising the numerator and the denominator separately to the power indicated
a root - the index of which is r.
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

40. 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.
0 exponent
The law of exponents for division
Positive
what power is intended and what root is intended

41. 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
vinculum
keep the fraction in that form rather than express it as a mixed number
Does not Exist

42. Any number divided by itself results in a _________ and has a value of 1
0 exponent
Zero occurs as an exponent
Imaginary Number
the rule for fractional exponents to solve problems

43. A fraction is raised to a power by
A root of a number
Raising the numerator and the denominator separately to the power indicated
One desired
Positive

44. The law of exponents for a power of an indicated quotient
The process of taking a root of a number
The process of finding a root
vinculum
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.

45. The line above the number whose root is to be found is a symbol of grouping called the
vinculum
number of minus signs
keep the fraction in that form rather than express it as a mixed 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.

46. To divide one power into another having the same base
zero power
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.
The power

47. Is the number of times the number itself is to be taken as a factor.
The power
The process of finding a root
Raising the numerator and the denominator separately to the power indicated
zero power

48. We recall that the exponent of a number tells
A root of a number
The number of times that the number is to be taken as a factor
The operation of raising a number to a power
a root - the index of which is r.

49. To determine the number of decimal places in the root of a perfect power
The law of exponents for division may be developed from this example
zero power
Divide the number of decimal places in the radicand by the index of the root.
When the radical symbol is used