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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. Is a special factor of a number.
its value is 1
A root
The laws of exponents
The number of times that the number is to be taken as a factor

2. The sign of the product is determined - as in ordinary multiplication - by the
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.
Raising the numerator and the denominator separately to the power indicated
number of minus signs

3. The indicated square root of a negative number is called an
Imaginary Number
Zero occurs as an exponent
The number itself
The law of exponents for division

4. Any number divided by itself is
merely moving the expression which contains the exponent to the other position in the fraction
Divide the number of decimal places in the radicand by the index of the root.
1
the power is negative

5. To determine the number of decimal places in the root of a perfect power
Divide the number of decimal places in the radicand by the index of the root.
0 exponent
the power is negative
The law of exponents for division

6. 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 number of minus signs is odd or even -
One desired
Positive
The law of exponents for division may be developed from this example

7. 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
The number of minus signs is odd or even -
number of minus signs
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.

8. Is the number of times the number itself is to be taken as a factor.
number of minus signs
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
The power

9. If an improper fraction occurs in an exponent it is customary to
A root
keep the fraction in that form rather than express it as a mixed number
zero power
The law of exponents for division

10. The line above the number whose root is to be found is a symbol of grouping called the
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.
vinculum
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.

11. A fractional exponent of the form 1/r indicates
INDEX of the root
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.
negative exponents arise
a root - the index of which is r.

12. To multiply two or more powers having the same base -
Zero occurs as an exponent
Add the exponents and raise the common base to the sum of the exponents
Raising the numerator and the denominator separately to the power indicated
its value is 1

13. The law of exponents for multiplication may be stated as follows:
0 exponent
the rule for fractional exponents to solve problems
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.

14. The square of a real number is
Positive
negative exponents arise
A root of a number
Raising to a power

15. The number that indicates the root is called the
Add the exponents and raise the common base to the sum of the exponents
0 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.
INDEX of the root

16. The power of a product is equal to the product obtained when
The process of taking a root of a number
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
The operation of raising a number to a power
Is equal to the number of places in the decimal multiplied by the exponent.

17. A fraction is raised to a power by
The number itself
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
Raising the numerator and the denominator separately to the power indicated
When the radical symbol is used

18. Is the inverse of raising a number to a power.
zero power
The process of taking a root of a number
INDEX of the root
The process of finding a root

19. 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.
Positive
Exponent
The process of taking 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.

20. Any number divided by itself results in a _________ and has a value of 1
0 exponent
its value is 1
The process of taking a root of a number
Decimal places in the factors together

21. Finding a root of a number is
The process of finding a root
Decimal places in the factors together
The process of taking a root of a number
The inverse of raising a number to a power.

22. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
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.
number of minus signs
negative exponents arise
A root of a number

23. When the exponent of a negative number is odd -
The number of minus signs is odd or even -
the power is negative
Does not Exist
Raising the numerator and the denominator separately to the power indicated

24. Notice that the sign of an exponent may be changed by
The process of finding a root
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
The law of exponents for division

25. In the answer to a problem such as 4^3 + 4^3.
The power
Zero occurs as an exponent
Exponent
Raising the numerator and the denominator separately to the power indicated

26. We recall that the exponent of a number tells
its value is 1
The process of taking a root of a number
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

27. In fraction form an exponent shows immediately
The power
what power is intended and what root is intended
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.

28. Depending on whether the exponent of the base is odd or even.
The number of minus signs is odd or even -
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
zero power

29. The laws of exponents for the power of a power may be stated as follows:
The power
the power is 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.
Positive

30. 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.
Raising to a power
number of minus signs
The law of exponents for division may be developed from this example

31. Is multiplication in which all the numbers being multiplied together are equal.
Raising to a power
The number of minus signs is odd or even -
Add the exponents and raise the common base to the sum of the exponents
the rule for fractional exponents to solve problems

32. To divide one power into another having the same base
A root
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.
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

33. The law of exponents for multiplication may be combined with
INDEX of the root
the rule for fractional exponents to solve problems
0 exponent
Exponent

34. It is important to realize that the base must be the same for each factor - in order to apply
The laws of exponents
The number of times that the number is to be taken as a factor
Imaginary Number
Is equal to the number of places in the decimal multiplied by the exponent.

35. When the exponent is even
Positive
Decimal places in the factors together
The process of finding a root
the power is positive

36. 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 law of exponents for division may be developed from this example
what power is intended and what root is intended
One desired
A root of a number

37. The first power of any number is
Does not Exist
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
merely moving the expression which contains the exponent to the other position in the fraction
The number itself

38. When an exponent occurs - it must always be written unless...
Decimal places in the factors together
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
A root
its value is 1

39. Is a special case of multiplication in which the factors are all equal.
The inverse of raising a number to a power.
The operation of raising a number to a power
Raising 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.

40. Any number (other than zero) raised to the _____ equals 1
The law of exponents for division
The number of times that the number is to be taken as a factor
zero power
Real Numbers

41. The law of exponents for the power of a product is as follows:
what power is intended and what root is intended
A root of a number
Is equal to the number of places in the decimal multiplied by the 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.

42. 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.
Divide the number of decimal places in the radicand by the index of the root.
Add the exponents and raise the common base to the sum of the exponents
The law of exponents for division
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. When a decimal is raised to a power - the number of decimal places in the result
The number of minus signs is odd or even -
Is equal to the number of places in the decimal multiplied by the exponent.
The number of times that the number is to be taken as a factor
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.

44. Positive and negative numbers belong to the class called
Divide the number of decimal places in the radicand by the index of the root.
Imaginary Number
Real Numbers
a root - the index of which is r.

45. When a radical has no index - the square root is understood to be the
vinculum
Decimal places in the factors together
One desired
the rule for fractional exponents to solve problems

46. 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 laws of exponents
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
number of minus signs

47. 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.
1
The operation of raising a number to a power
Exponent
Zero occurs as an exponent

48. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
Real Numbers
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.
1
A root

49. Mark off as many decimal places in the product as there are
Decimal places in the factors together
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
zero power
The number itself