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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. When the exponent of a negative number is odd -
The process of taking a root of a number
Imaginary Number
the power is negative
0 exponent

2. 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.
Zero occurs as an exponent
0 exponent
A root
Exponent

3. Is a special case of multiplication in which the factors are all equal.
A root
The operation of raising a number to a power
The process of finding a root
vinculum

4. The laws of exponents for the power of a power may be stated as follows:
Imaginary Number
vinculum
the rule for fractional exponents to solve problems
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.

5. The law of exponents for multiplication may be stated as follows:
One desired
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.
Is equal to the number of places in the decimal multiplied by the exponent.

6. When an exponent occurs - it must always be written unless...
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
what power is intended and what root is intended
its value is 1

7. In the answer to a problem such as 4^3 + 4^3.
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.
Zero occurs as an exponent
Divide the number of decimal places in the radicand by the index of the root.

8. A fraction is raised to a power by
The power
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
Raising to a power

9. When a radical has no index - the square root is understood to be the
Raising the numerator and the denominator separately to the power indicated
One desired
Exponent
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

10. To divide one power into another having the same base
the rule for fractional exponents to solve problems
a root - the index of which is r.
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 law of exponents for division

11. 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.
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.
Positive
One desired

12. 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.
One desired
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

13. Any number divided by itself is
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
1
Decimal places in the factors together
the power is negative

14. The line above the number whose root is to be found is a symbol of grouping called the
vinculum
Decimal places in the factors together
A root
keep the fraction in that form rather than express it as a mixed number

15. 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.
Add the exponents and raise the common base to the sum of the exponents
INDEX of the root
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 law of exponents for division

16. When the exponent is even
the power is positive
negative exponents arise
1
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

17. Is the inverse of raising a number to a power.
Exponent
The process of finding a root
The process of taking a root of a number
The law of exponents for division

18. When a decimal is raised to a power - the number of decimal places in the result
Add the exponents and raise the common base to the sum of the exponents
its value is 1
Is equal to the number of places in the decimal multiplied by the exponent.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

19. 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.
Does not Exist
its value is 1
A root of a number
vinculum

20. Positive and negative numbers belong to the class called
Exponent
Decimal places in the factors together
Real Numbers
the power is positive

21. It is important to realize that the base must be the same for each factor - in order to apply
Does not Exist
negative exponents arise
The laws of exponents
Imaginary Number

22. Is multiplication in which all the numbers being multiplied together are equal.
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.
Raising to a power
vinculum

23. To multiply two or more powers having the same base -
Real Numbers
The power
The law of exponents for division
Add the exponents and raise the common base to the sum of the exponents

24. Is a special factor of a number.
Raising to a power
Raising the numerator and the denominator separately to the power indicated
A root
Decimal places in the factors together

25. We recall that the exponent of a number tells
The number itself
merely moving the expression which contains the exponent to the other position in the fraction
The number of times that the number is to be taken as a factor
Add the exponents and raise the common base to the sum of the exponents

26. Is the number of times the number itself is to be taken as a factor.
its value is 1
The power
number of minus signs
The number itself

27. To determine the number of decimal places in the root of a perfect power
the rule for fractional exponents to solve problems
The operation of raising a number to a power
Divide the number of decimal places in the radicand by the index of the root.
Imaginary Number

28. The law of exponents for multiplication may be combined with
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
a root - the index of which is r.
the power is positive
the rule for fractional exponents to solve problems

29. Any number (other than zero) raised to the _____ equals 1
The operation of raising a number to a power
A root of a number
1
zero power

30. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
its value is 1
Does not Exist
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

31. Finding a root of a number is
A root of a number
a root - the index of which is r.
The inverse of raising a number to a power.
The laws of exponents

32. 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
Does not Exist
When the radical symbol is used
A root of a number

33. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
negative exponents arise
The power
The process of finding a root
The number itself

34. 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.
Raising the numerator and the denominator separately to the power indicated
Is equal to the number of places in the decimal multiplied by the exponent.
The process of taking a root of a number

35. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
The law of exponents for division may be developed from this example
what power is intended and what root is intended
the power is positive
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.

36. 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
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
Raising to a power

37. The number that indicates the root is called the
A root of a number
Positive
The inverse of raising a number to a power.
INDEX of the root

38. The sign of the product is determined - as in ordinary multiplication - by the
0 exponent
number of minus signs
The number of minus signs is odd or even -
When the radical symbol is used

39. In fraction form an exponent shows immediately
Zero occurs as an exponent
the power is positive
Does not Exist
what power is intended and what root is intended

40. 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
its value is 1
Real Numbers
the rule for fractional exponents to solve problems

41. Any number divided by itself results in a _________ and has a value of 1
the rule for fractional exponents to solve problems
0 exponent
zero power
Real Numbers

42. 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.
One desired
a root - the index of which is r.
A root

43. If an improper fraction occurs in an exponent it is customary to
A 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.
its value is 1
keep the fraction in that form rather than express it as a mixed number

44. Depending on whether the exponent of the base is odd or even.
what power is intended and what root is intended
One desired
The number of minus signs is odd or even -
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

45. The indicated square root of a negative number is called an
Imaginary Number
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 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

46. The power of a product is equal to the product obtained when
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
Raising to a power
0 exponent

47. The first power of any number is
Zero occurs as an exponent
the power is positive
Imaginary Number
The number itself

48. 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 law of exponents for division
the power is positive
Raising the numerator and the denominator separately to the power indicated
The process of taking a root of a number

49. Mark off as many decimal places in the product as there are
Decimal places in the factors 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.
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.
vinculum