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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 is even
The power
Imaginary Number
the power is positive
Divide the number of decimal places in the radicand by the index of the root.

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

3. When the exponent of a negative number is odd -
the power is negative
The process of taking a root of a number
The process of finding a root
merely moving the expression which contains the exponent to the other position in the fraction

4. Is multiplication in which all the numbers being multiplied together are equal.
A root of a number
When the radical symbol is used
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Raising to a power

5. Is the number of times the number itself is to be taken as a factor.
The power
the rule for fractional exponents to solve problems
The number of times that the number is to be taken as a factor
The law of exponents for division

6. To determine the number of decimal places in the root of a perfect power
Raising the numerator and the denominator separately to the power indicated
The inverse of raising a number to a power.
Divide the number of decimal places in the radicand by the index of the root.
The number of minus signs is odd or even -

7. The law of exponents for a power of an indicated quotient
Raising 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.
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 rule for fractional exponents to solve problems

8. 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 laws of exponents
Add the exponents and raise the common base to the sum of the exponents
The number of minus signs is odd or even -

9. 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.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Imaginary Number
The law of exponents for division
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.

10. Any number (other than zero) raised to the _____ equals 1
Exponent
its value is 1
The number of times that the number is to be taken as a factor
zero power

11. 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 number of times that the number is to be taken as a factor
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.
A root of a number
Divide the number of decimal places in the radicand by the index of the root.

12. The sign of the product is determined - as in ordinary multiplication - by the
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 minus signs is odd or even -
number of minus signs
1

13. When an exponent occurs - it must always be written unless...
A root of a number
negative exponents arise
its value is 1
The process of finding a root

14. In fraction form an exponent shows immediately
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.
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.
The number itself

15. Notice that the sign of an exponent may be changed by
its value is 1
merely moving the expression which contains the exponent to the other position in the fraction
what power is intended and what root is intended
Is equal to the number of places in the decimal multiplied by the exponent.

16. Any number divided by itself results in a _________ and has a value of 1
The laws of exponents
its value is 1
0 exponent
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 a special case of multiplication in which the factors are all equal.
The process of taking a root of a number
the rule for fractional exponents to solve problems
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 operation of raising a number to a power

18. The law of exponents for multiplication may be stated as follows:
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.
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 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.

19. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
the rule for fractional exponents to solve problems
When the radical symbol is used
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

20. The indicated square root of a negative number is called an
The number of minus signs is odd or even -
0 exponent
INDEX of the root
Imaginary Number

21. To multiply two or more powers having the same base -
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
Real Numbers

22. 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
a root - the index of which is r.
number of minus signs
One desired

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

24. A fraction is raised to a power by
Does not Exist
Raising the numerator and the denominator separately to the power indicated
A root of a number
0 exponent

25. We recall that the exponent of a number tells
The number of times that the number is to be taken as a factor
Raising the numerator and the denominator separately to the power indicated
The process of finding a root
the rule for fractional exponents to solve problems

26. 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.
Raising the numerator and the denominator separately to the power indicated
The operation of raising a number to a power
1

27. A fractional exponent of the form 1/r indicates
a root - the index of which is r.
INDEX of the root
Add the exponents and raise the common base to the sum of the exponents
zero power

28. 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
The process of taking a root of a number
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.
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

29. When a radical has no index - the square root is understood to be the
the power is positive
the power is negative
Imaginary Number
One desired

30. The law of exponents for multiplication may be combined with
the rule for fractional exponents to solve problems
Decimal places in the factors together
the power is negative
Raising to a power

31. In the answer to a problem such as 4^3 + 4^3.
The inverse of raising a number to a power.
Raising to a power
INDEX of the root
Zero occurs as an exponent

32. Depending on whether the exponent of the base is odd or even.
A root of a number
Decimal places in the factors together
The number of minus signs is odd or even -
negative exponents arise

33. Any number divided by itself is
1
zero power
The power
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.

34. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
zero power
A root of a number
Is equal to the number of places in the decimal multiplied by the exponent.
negative exponents arise

35. The first power of any number is
The number of times that the number is to be taken as a factor
Raising to a power
negative exponents arise
The number itself

36. It is important to realize that the base must be the same for each factor - in order to apply
number of minus signs
A root of a number
The laws of exponents
INDEX of the root

37. Is the inverse of raising a number to a power.
The process of finding a root
The laws of 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.
Positive

38. The number that indicates the root is called the
what power is intended and what root is intended
Exponent
INDEX of the root
Does not Exist

39. The law of exponents for the power of a product is as follows:
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
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.

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

41. Is a special factor of a number.
INDEX of the root
Divide the number of decimal places in the radicand by the index of the root.
A root
The laws of exponents

42. The square of a real number is
The laws of exponents
merely moving the expression which contains the exponent to the other position in the fraction
Positive
The operation of raising a number to a power

43. To divide one power into another having the same base
1
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.
Exponent

44. 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.
Exponent
The inverse of raising a number to a power.
The law of exponents for division may be developed from this example
vinculum

45. 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
The number of times that the number is to be taken as a factor
vinculum

46. 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 -
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.
a root - the index of which is r.
Exponent

47. Positive and negative numbers belong to the class called
Is equal to the number of places in the decimal multiplied by the exponent.
Add the exponents and raise the common base to the sum of the exponents
When the radical symbol is used
Real Numbers

48. When a decimal is raised to a power - the number of decimal places in the result
vinculum
Raising the numerator and the denominator separately to the power indicated
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.
Is equal to the number of places in the decimal multiplied by the exponent.

49. Mark off as many decimal places in the product as there are
Exponent
Add the exponents and raise the common base to the sum of the exponents
Decimal places in the factors together
number of minus signs