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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. Finding a root of a number is
The number of minus signs 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 law of exponents for division may be developed from this example

2. The law of exponents for the power of a product is as follows:
Raising the numerator and the denominator separately to the power indicated
The number itself
The number of minus signs is odd or even -
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.

3. Any number divided by itself is
the power is positive
The operation of raising a number to a power
1
Imaginary Number

4. Mark off as many decimal places in the product as there are
Zero occurs as an exponent
Decimal places in the factors together
zero power
The power

5. Depending on whether the exponent of the base is odd or even.
number of minus signs
The number of minus signs is odd or even -
A 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.

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

7. 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
Raising to a power
what power is intended and what root is intended
Does not Exist

8. The sign of the product is determined - as in ordinary multiplication - by the
number of minus signs
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.
Zero occurs as an exponent

9. 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 -
Decimal places in the factors together
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.

10. The first power of any number is
a root - the index of which is r.
The number itself
The law of exponents for division may be developed from this example
A root of a number

11. Positive and negative numbers belong to the class called
Real Numbers
The process of finding a root
Imaginary Number
Decimal places in the factors together

12. When the exponent of a negative number is odd -
merely moving the expression which contains the exponent to the other position in the fraction
the power is negative
The law of exponents for division
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

13. Is multiplication in which all the numbers being multiplied together are equal.
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 itself
Raising to a power
When the radical symbol is used

14. When an exponent occurs - it must always be written unless...
Decimal places in the factors together
its value is 1
When the radical symbol is used
a root - the index of which is r.

15. 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
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
0 exponent
number of minus signs

16. The laws of exponents for the power of a power may be stated as follows:
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.
The operation of raising a number to a power
its value is 1

17. 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
Raising the numerator and the denominator separately to the power indicated
Real Numbers

18. The square of a real number is
When the radical symbol is used
The process of finding a root
Positive
A root of a number

19. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
the power is positive
The number of times that the number is to be taken as a factor
Decimal places in the factors together
negative exponents arise

20. The law of exponents for multiplication may be stated as follows:
The operation of raising a number 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.
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 of times that the number is to be taken as a factor

21. 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.
The operation 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 law of exponents for division

22. When a radical has no index - the square root is understood to be the
The number itself
Add the exponents and raise the common base to the sum of the exponents
One desired
Divide the number of decimal places in the radicand by the index of the root.

23. A fractional exponent of the form 1/r indicates
a root - the index of which is r.
A root of a number
The law of exponents for division may be developed from this example
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.

24. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
the power is positive
The inverse of raising a number to a power.
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.
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.

25. 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.
Add the exponents and raise the common base to the sum of the exponents
Decimal places in the factors together
The law of exponents for division may be developed from this example
The laws of exponents

26. Is a special factor of a number.
A root
the power is negative
Does not Exist
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.

27. When the exponent is even
The law of exponents for division
Exponent
Raising to a power
the power is positive

28. 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.
Positive
the power is negative
what power is intended and what root is intended
The law of exponents for division

29. If an improper fraction occurs in an exponent it is customary to
The process of finding a root
A root
keep the fraction in that form rather than express it as a mixed number
Zero occurs as an exponent

30. The power of a product is equal to the product obtained when
The number of times that the number is to be taken as a factor
The process of finding a root
A root
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

31. It is important to realize that the base must be the same for each factor - in order to apply
The laws of exponents
INDEX of the root
0 exponent
Zero occurs as an exponent

32. In fraction form an exponent shows immediately
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.
what power is intended and what root is intended
The law of exponents for division may be developed from this example
The number of times that the number is to be taken as a factor

33. Is the inverse of raising a number to a power.
Decimal places in the factors together
The number of times that the number is to be taken as a factor
The process of finding a root
1

34. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
vinculum
zero power
A root of a number
When the radical symbol is used

35. 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 rule for fractional exponents to solve problems
A root of a number
negative exponents arise
1

36. In the answer to a problem such as 4^3 + 4^3.
Zero occurs as an exponent
The law of exponents for division may be developed from this example
what power is intended and what root is intended
The law of exponents for division

37. Is a special case of multiplication in which the factors are all equal.
INDEX of the root
When the radical symbol is used
a root - the index of which is r.
The operation of raising a number to a power

38. The number that indicates the root is called the
Positive
A root of a number
INDEX of the root
its value is 1

39. The law of exponents for a power of an indicated quotient
The laws of exponents
Real Numbers
number of minus signs
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. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Does not Exist
Decimal places in the factors together
A root

41. Any number (other than zero) raised to the _____ equals 1
Raising to a power
what power is intended and what root is intended
0 exponent
zero power

42. Any number divided by itself results in a _________ and has a value of 1
merely moving the expression which contains the exponent to the other position in the fraction
0 exponent
Raising the numerator and the denominator separately to the power indicated
A root of a number

43. The indicated square root of a negative number is called an
Raising the numerator and the denominator separately to the power indicated
Imaginary Number
the power is positive
Real Numbers

44. Is the number of times the number itself is to be taken as a factor.
Decimal places in the factors together
The power
keep the fraction in that form rather than express it as a mixed number
a root - the index of which is r.

45. 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.
its value is 1
1
The operation of raising a number to a power
Exponent

46. We recall that the exponent of a number tells
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 is positive
The number of times that the number is to be taken as a factor
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

47. 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.
Zero occurs as an exponent
Positive
The number of times that the number is to be taken as a factor

48. The line above the number whose root is to be found is a symbol of grouping called the
vinculum
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.
Decimal places in the factors together

49. A fraction is raised to a power by
The number of minus signs is odd or even -
Raising the numerator and the denominator separately to the power indicated
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.
Raising to a power