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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. The law of exponents for the power of a product is as follows:
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
Positive
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

2. The law of exponents for multiplication may be combined with
the rule for fractional exponents to solve problems
Divide the number of decimal places in the radicand by the index of the root.
a root - the index of which is r.
Add the exponents and raise the common base to the sum of the exponents

3. Positive and negative numbers belong to the class called
INDEX of the root
Real Numbers
what power is intended and what root is intended
Positive

4. Finding a root of a number is
what power is intended and what root is intended
The inverse of raising a number to a power.
0 exponent
number of minus signs

5. 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 number of minus signs is odd or even -
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.
Raising the numerator and the denominator separately to the power indicated

6. When the exponent is even
Decimal places in the factors together
the power is positive
Zero occurs as an exponent
A root

7. We recall that the exponent of a number tells
The number of minus signs is odd or even -
Positive
1
The number of times that the number is to be taken as a factor

8. The square of a real number is
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.
Positive
the power is positive
INDEX of the root

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

10. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
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.
The number itself
number of minus signs

11. The number that indicates the root is called the
0 exponent
Does not Exist
INDEX of the root
the power is negative

12. Mark off as many decimal places in the product as there are
vinculum
The process of taking a root of a number
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.

13. A fraction is raised to a power by
The law of exponents for division may be developed from this example
The law of exponents for division
Zero occurs as an exponent
Raising the numerator and the denominator separately to the power indicated

14. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
INDEX of the root
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Add the exponents and raise the common base to the sum of the exponents
negative exponents arise

15. Is a special factor of a number.
The number of minus signs is odd or even -
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.
A root

16. When a decimal is raised to a power - the number of decimal places in the result
To multiply two or more powers having the same base - 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.
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 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. The sign of the product is determined - as in ordinary multiplication - by the
number of minus signs
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.
vinculum

18. 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 law of exponents for division may be developed from this example
Real Numbers
The law of exponents for division
Does not Exist

19. When an exponent occurs - it must always be written unless...
Zero occurs as an exponent
its value is 1
Add the exponents and raise the common base to the sum of the exponents
the power is negative

20. Is the number of times the number itself is to be taken as a factor.
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 power
INDEX of the root

21. 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.
vinculum
A root
zero power

22. 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
The process of taking a root of a number
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.

23. The indicated square root of a negative number is called an
The number of minus signs is odd or even -
the power is positive
Is equal to the number of places in the decimal multiplied by the exponent.
Imaginary Number

24. In the answer to a problem such as 4^3 + 4^3.
The process of finding a root
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.
keep the fraction in that form rather than express it as a mixed number

25. The first power of any number is
negative exponents arise
a root - the index of which is r.
The number itself
Does not Exist

26. 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
The law of exponents for division may be developed from this example
Divide the number of decimal places in the radicand by the index of the root.
A root

27. When a radical has no index - the square root is understood to be the
The power
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
One desired
vinculum

28. 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
A root of a number
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.
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.

29. Is the inverse of raising a number to a power.
a root - the index of which is r.
The process of finding a root
Imaginary Number
The law of exponents for division

30. Any number divided by itself is
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.
1
The process of finding a root
The operation of raising a number to a power

31. Is multiplication in which all the numbers being multiplied together are equal.
Raising to a power
Exponent
keep the fraction in that form rather than express it as a mixed number
merely moving the expression which contains the exponent to the other position in the fraction

32. It is important to realize that the base must be the same for each factor - in order to apply
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 laws of exponents
The number itself
the rule for fractional exponents to solve problems

33. Any number divided by itself results in a _________ and has a value of 1
0 exponent
The power
the power is negative
A root of a number

34. 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.
zero power
The law of exponents for division
The inverse of raising a number to a power.
what power is intended and what root is intended

35. The laws of exponents for the power of a power may be stated as follows:
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 inverse of raising a number to a power.
Exponent
INDEX of the root

36. To divide one power into another having the same base
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.
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.

37. The law of exponents for multiplication may be stated as follows:
the power is negative
The law of exponents for division may be developed from this example
One desired
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

38. To determine the number of decimal places in the root of a perfect power
INDEX of the root
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
0 exponent
Divide the number of decimal places in the radicand by the index of the root.

39. When the exponent of a negative number is odd -
negative exponents arise
Real Numbers
the power is negative
A root of a number

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.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
the power is positive
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 process of taking a root of a number

41. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
The operation of raising a number to a power
When the radical symbol is used
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.
keep the fraction in that form rather than express it as a mixed number

42. The line above the number whose root is to be found is a symbol of grouping called the
1
vinculum
Divide the number of decimal places in the radicand by the 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.

43. Notice that the sign of an exponent may be changed by
The number itself
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
merely moving the expression which contains the exponent to the other position in the fraction
The process of finding a root

44. A fractional exponent of the form 1/r indicates
Positive
a root - the index of which is r.
Real Numbers
The number of times that the number is to be taken as a factor

45. 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
When the radical symbol is used
vinculum
0 exponent

46. The law of exponents for a power of an indicated quotient
Divide the number of decimal places in the radicand by the 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.
The process of taking a root of a number
When the radical symbol is used

47. Depending on whether the exponent of the base is odd or even.
keep the fraction in that form rather than express it as a mixed number
Is equal to the number of places in the decimal multiplied by the exponent.
The number of minus signs is odd or even -
Does not Exist

48. In fraction form an exponent shows immediately
the power is negative
Positive
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.

49. Is a special case of multiplication in which the factors are all equal.
The operation of raising a number to a power
Divide the number of decimal places in the radicand by the index of the root.
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.