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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. To determine the number of decimal places in the root of a perfect power
Imaginary Number
1
vinculum
Divide the number of decimal places in the radicand by the index of the root.

2. When a radical has no index - the square root is understood to be the
One desired
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 process of finding a root

3. Mark off as many decimal places in the product as there are
The number of minus signs is odd or even -
keep the fraction in that form rather than express it as a mixed number
negative exponents arise
Decimal places in the factors together

4. A fraction is raised to a power by
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
its value is 1
Raising the numerator and the denominator separately to the power indicated
Does not Exist

5. The number that indicates the root is called the
Raising the numerator and the denominator separately to the power indicated
INDEX of the root
The number itself
The inverse of raising a number to a power.

6. To multiply two or more powers having the same base -
Exponent
Add the exponents and raise the common base to the sum of the exponents
One desired
A root

7. 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 laws of exponents
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 may be developed from this example
When the radical symbol is used

8. The sign of the product is determined - as in ordinary multiplication - by the
A root of a number
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
the rule for fractional exponents to solve problems
number of minus signs

9. 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.
Positive
The power
the power is negative
A root of a number

10. We recall that the exponent of a number tells
The power
The number of times that the number is to be taken as a factor
Real Numbers
One desired

11. Finding a root of a number is
The inverse of raising a number to a power.
0 exponent
vinculum
The process of finding a root

12. Is the inverse of raising a number to a power.
The process of finding a root
The inverse of raising a number to a power.
The power
Divide the number of decimal places in the radicand by the index of the root.

13. When the exponent of a negative number is odd -
the power is negative
The operation of raising a number to a power
A root of a number
Raising the numerator and the denominator separately to the power indicated

14. When the exponent is even
The number of minus signs is odd or even -
the power is positive
The operation of raising a number to a power
negative exponents arise

15. 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
The process of finding a root
Is equal to the number of places in the decimal multiplied by the exponent.
The laws of exponents

16. It is important to realize that the base must be the same for each factor - in order to apply
The number itself
The laws of exponents
Add the exponents and raise the common base to the sum of the exponents
a root - the index of which is r.

17. To divide one power into another having the same base
Imaginary Number
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
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.
When the radical symbol is used

18. The indicated square root of a negative number is called an
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.
Imaginary Number
Exponent
a root - the index of which is r.

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

20. Depending on whether the exponent of the base is odd or even.
The number itself
The inverse of raising a number to a power.
the power is positive
The number of minus signs is odd or even -

21. Is a special case of multiplication in which the factors are all equal.
keep the fraction in that form rather than express it as a mixed number
Positive
The operation of raising a number to a power
the power is negative

22. Any number divided by itself results in a _________ and has a value of 1
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
0 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.

23. Is a special factor of a number.
The law of exponents for division may be developed from this example
number of minus signs
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
A root

24. The law of exponents for multiplication may be stated as follows:
The inverse of raising a number to a power.
negative exponents arise
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

25. In the answer to a problem such as 4^3 + 4^3.
The number itself
Raising to a power
The number of times that the number is to be taken as a factor
Zero occurs as an exponent

26. Is multiplication in which all the numbers being multiplied together are equal.
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.
INDEX of the root
Raising to a power
Does not Exist

27. A fractional exponent of the form 1/r indicates
The power
Decimal places in the factors together
the rule for fractional exponents to solve problems
a root - the index of which is r.

28. Positive and negative numbers belong to the class called
Is equal to the number of places in the decimal multiplied by the exponent.
what power is intended and what root is intended
Real Numbers
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.

29. The law of exponents for multiplication may be combined with
The law of exponents for division may be developed from this example
the rule for fractional exponents to solve problems
The laws of exponents
One desired

30. The power of a product is equal to the product obtained when
A root
0 exponent
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
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.

31. Is the number of times the number itself is to be taken as a factor.
The power
the power is negative
Decimal places in the factors together
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.

32. 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
keep the fraction in that form rather than express it as a mixed number
the power is positive
Divide the number of decimal places in the radicand by the index of the root.

33. Any number (other than zero) raised to the _____ equals 1
zero power
The process of taking a root of a number
1
Decimal places in the factors together

34. Notice that the sign of an exponent may be changed by
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
negative exponents arise
The laws of exponents
merely moving the expression which contains the exponent to the other position in the fraction

35. If an improper fraction occurs in an exponent it is customary to
the power is negative
zero power
keep the fraction in that form rather than express it as a mixed number
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

36. The law of exponents for the power of a product is as follows:
Exponent
The number of times that the number is to be taken as a factor
The process of finding a root
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.

37. 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
number of minus signs
what power is intended and what root is intended
The law of exponents for division

38. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
The power
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.
its value is 1

39. The line above the number whose root is to be found is a symbol of grouping called the
keep the fraction in that form rather than express it as a mixed number
the power is negative
vinculum
The laws of exponents

40. Any number divided by itself is
The laws of exponents
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 to a power
1

41. 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
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.
The process of finding a root

42. When an exponent occurs - it must always be written unless...
Divide the number of decimal places in the radicand by the index of the root.
its value is 1
A root of a number
One desired

43. The law of exponents for a power of an indicated quotient
The law of exponents for division
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.
The number itself

44. The square of a real number is
Positive
Add the exponents and raise the common base to the sum of the exponents
keep the fraction in that form rather than express it as a mixed number
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

45. 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.
the power is negative
Zero occurs as an exponent
keep the fraction in that form rather than express it as a mixed number

46. The first power of any number is
Divide the number of decimal places in the radicand by the index of the root.
the power is negative
merely moving the expression which contains the exponent to the other position in the fraction
The number itself

47. In fraction form an exponent shows immediately
0 exponent
The process of taking a root of a number
what power is intended and what root is intended
The process of finding a root

48. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
The process of finding a root
The number of times that the number is to be taken as a factor
vinculum
negative exponents arise

49. When a decimal is raised to a power - the number of decimal places in the result
When the radical symbol is used
number of minus signs
vinculum
Is equal to the number of places in the decimal multiplied by the exponent.