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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. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
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 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
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.

2. When a radical has no index - the square root is understood to be the
number of minus signs
Exponent
One desired
merely moving the expression which contains the exponent to the other position in the fraction

3. If an improper fraction occurs in an exponent it is customary to
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
The process of finding a root
the rule for fractional exponents to solve problems

4. It is important to realize that the base must be the same for each factor - in order to apply
When the radical symbol is used
merely moving the expression which contains the exponent to the other position in the fraction
The operation of raising a number to a power
The laws of exponents

5. Finding a root of a number is
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
The inverse of raising a number to a power.
merely moving the expression which contains the exponent to the other position in the fraction
The number of minus signs is odd or even -

6. Depending on whether the exponent of the base is odd or even.
negative exponents arise
Positive
what power is intended and what root is intended
The number of minus signs is odd or even -

7. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
The law of exponents for division
A root of a number
When the radical symbol is used
number of minus signs

8. The power of a product is equal to the product obtained when
1
Imaginary Number
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

9. The indicated square root of a negative number is called an
The number of minus signs is odd or even -
The operation of raising a number to a power
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.
Imaginary Number

10. Positive and negative numbers belong to the class called
1
A root of a number
its value is 1
Real Numbers

11. The law of exponents for the power of a product is as follows:
The inverse of raising a number to a power.
number of minus signs
Does not Exist
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.

12. Any number divided by itself results in a _________ and has a value of 1
negative exponents arise
0 exponent
Does not Exist
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. Mark off as many decimal places in the product as there are
Decimal places in the factors together
what power is intended and what root is intended
its value is 1
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.

14. Any number divided by itself is
1
The number itself
a root - the index of which is r.
Real Numbers

15. The law of exponents for a power of an indicated quotient
The number of times that the number is to be taken as a factor
Decimal places in the factors together
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.

16. Any number (other than zero) raised to the _____ equals 1
zero power
Raising to a power
0 exponent
The process of finding a root

17. The line above the number whose root is to be found is a symbol of grouping called the
The inverse of raising a number to a power.
its value is 1
The number of minus signs is odd or even -
vinculum

18. A fraction is raised to a power by
Is equal to the number of places in the decimal multiplied by the exponent.
Raising the numerator and the denominator separately to the power indicated
A root of a number
the rule for fractional exponents to solve problems

19. When an exponent occurs - it must always be written unless...
number of minus signs
its value is 1
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.
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.

20. 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 may be developed from this example
The power
the power is positive
vinculum

21. The law of exponents for multiplication may be combined with
Real Numbers
Does not Exist
the power is positive
the rule for fractional exponents to solve problems

22. The first power of any number is
The number of minus signs is odd or even -
The law of exponents for division
The number itself
what power is intended and what root is intended

23. The sign of the product is determined - as in ordinary multiplication - by the
vinculum
number of minus signs
Add the exponents and raise the common base to the sum of the exponents
The number of times that the number is to be taken as a factor

24. When the exponent of a negative number is odd -
the power is negative
The law of exponents for division
Raising the numerator and the denominator separately to the power indicated
A root

25. Is the inverse of raising a number to a power.
One desired
the power is positive
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 process of finding a root

26. 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.
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.
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.
what power is intended and what root is intended

27. 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.
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.
Exponent
1

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.
Zero occurs as an exponent
the rule for fractional exponents to solve problems
INDEX of the root
The law of exponents for division

29. Is the number of times the number itself 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.
The process of taking a root of a number
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

30. The law of exponents for multiplication may be stated as follows:
1
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.
negative exponents arise

31. In fraction form an exponent shows immediately
negative exponents arise
what power is intended and what root is intended
One desired
vinculum

32. Is a special factor of a number.
Positive
negative exponents arise
Zero occurs as an exponent
A root

33. 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.
Real Numbers
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
The process of taking a root of a number

34. A fractional exponent of the form 1/r indicates
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 number of times that the number is to be taken as a factor
number of minus signs
a root - the index of which is r.

35. When the exponent is even
the power is positive
The number itself
The operation of raising a number to a power
the power is negative

36. The number that indicates the root is called the
When the radical symbol is used
The law of exponents for division may be developed from this example
INDEX of the root
negative exponents arise

37. Notice that the sign of an exponent may be changed by
zero power
the power is negative
Does not Exist
merely moving the expression which contains the exponent to the other position in the fraction

38. To multiply two or more powers having the same base -
zero power
the power is negative
Add the exponents and raise the common base to the sum of the exponents
its value is 1

39. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
Decimal places in the factors together
Raising to a power
negative exponents arise

40. In the answer to a problem such as 4^3 + 4^3.
Zero occurs as an exponent
the power is negative
The power
The operation of raising a number to a power

41. Is a special case of multiplication in which the factors are all equal.
Is equal to the number of places in the decimal multiplied by the exponent.
Zero occurs as an exponent
The operation of raising a number to a power
Raising to a power

42. 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
Positive
its value is 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.

43. The square of a real number is
Positive
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.
Raising to a power
keep the fraction in that form rather than express it as a mixed number

44. 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.
1
what power is intended and what root is intended
One desired

45. We recall that the exponent of a number tells
the power is positive
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.
Exponent
The number of times that the number is to be taken as a factor

46. To determine the number of decimal places in the root of a perfect power
Imaginary Number
zero power
The laws of exponents
Divide the number of decimal places in the radicand by the index of the root.

47. 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
Does not Exist
vinculum
what power is intended and what root is intended

48. Is multiplication in which all the numbers being multiplied together are equal.
The laws of exponents
number of minus signs
Is equal to the number of places in the decimal multiplied by the exponent.
Raising to a power

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