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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. Is a special factor 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.
Decimal places in the factors together
Add the exponents and raise the common base to the sum of the exponents
A root

2. 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.
zero power
The inverse of raising a number to a power.
Imaginary Number

3. The law of exponents for multiplication may be stated as follows:
zero power
what power is intended and what root is intended
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
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.

4. The line above the number whose root is to be found is a symbol of grouping called the
The laws of exponents
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.
vinculum

5. Any number (other than zero) raised to the _____ equals 1
zero 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.
a root - the index of which is r.
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.

6. 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.
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.
Imaginary Number
Zero occurs as an exponent

7. The indicated square root of a negative number is called an
Imaginary Number
keep the fraction in that form rather than express it as a mixed number
The number of minus signs is odd or even -
INDEX of the root

8. 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 to a power
Exponent
The law of exponents for division may be developed from this example
Decimal places in the factors together

9. Is the number of times the number itself is to be taken as a factor.
The power
The law of exponents for division
merely moving the expression which contains the exponent to the other position in the fraction
Decimal places in the factors together

10. In the answer to a problem such as 4^3 + 4^3.
negative exponents arise
a root - the index of which is r.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Zero occurs as an exponent

11. 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.
Exponent
Raising to a power
zero power

12. The first power of any number is
Imaginary Number
The process of finding a root
The number itself
One desired

13. When an exponent occurs - it must always be written unless...
The number itself
0 exponent
its value is 1
Exponent

14. The law of exponents for multiplication may be combined with
the rule for fractional exponents to solve problems
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.
A root

15. In fraction form an exponent shows immediately
The process of finding a root
what power is intended and what root is intended
Decimal places in the factors together
negative exponents arise

16. When a decimal is raised to a power - the number of decimal places in the result
Zero occurs as an exponent
The process of finding a root
Is equal to the number of places in the decimal multiplied by the exponent.
The operation of raising a number to a power

17. 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
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.
what power is intended and what root is intended

18. It is important to realize that the base must be the same for each factor - in order to apply
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 laws of exponents
When the radical symbol is used
what power is intended and what root is intended

19. Notice that the sign of an exponent may be changed by
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
zero power
Raising the numerator and the denominator separately to the power indicated
merely moving the expression which contains the exponent to the other position in the fraction

20. The laws of exponents for the power of a power may be stated as follows:
The operation of raising a number to a power
a root - the index of which is r.
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.

21. A fractional exponent of the form 1/r indicates
The process of taking a root of a number
The number itself
a root - the index of which is r.
The number of times that the number is to be taken as a factor

22. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
negative exponents arise
The process of taking a root of a number
Divide the number of decimal places in the radicand by the index of the root.
Exponent

23. Is the inverse of raising a number to a power.
The process of finding 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.
number of minus signs
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. When the exponent of a negative number is odd -
Divide the number of decimal places in the radicand by the index of the root.
Does not Exist
negative exponents arise
the power is negative

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.
The process of finding a root
The number of times that the number is to be taken as a factor
number of minus signs
The law of exponents for division may be developed from this example

26. The number that indicates the root is called the
INDEX of the root
Zero occurs as an exponent
Does not Exist
Raising the numerator and the denominator separately to the power indicated

27. A fraction is raised to a power by
the power is positive
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.
Raising the numerator and the denominator separately to the power indicated

28. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
Is equal to the number of places in the decimal multiplied by the exponent.
Positive
When the radical symbol is used
vinculum

29. Is multiplication in which all the numbers being multiplied together are equal.
Imaginary Number
Does not Exist
Raising to a power
1

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

31. When a radical has no index - the square root is understood to be the
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
The inverse of raising a number to a power.
One desired

32. Any number divided by itself results in a _________ and has a value of 1
keep the fraction in that form rather than express it as a mixed number
0 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 is positive

33. Mark off as many decimal places in the product as there are
Decimal places in the factors together
Imaginary Number
the power is negative
Add the exponents and raise the common base to the sum of the exponents

34. The law of exponents for a power of an indicated quotient
the power is negative
vinculum
Zero occurs as an 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.

35. Is a special case of multiplication in which the factors are all equal.
The operation of raising a number to a power
Real Numbers
The process of taking a root of a number
The inverse of raising a number to a power.

36. 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
Decimal places in the factors together
Is equal to the number of places in the decimal multiplied by the exponent.
Real Numbers

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

38. The square of a real number is
Positive
0 exponent
Raising to a power
The number of minus signs is odd or even -

39. When the exponent is even
The law of exponents for division may be developed from this example
the power is positive
The inverse of raising a number to a power.
A root of a number

40. 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.
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.
its value is 1
A root of a number

41. Positive and negative numbers belong to the class called
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.
0 exponent
Real Numbers
The law of exponents for division

42. The sign of the product is determined - as in ordinary multiplication - by the
number of minus signs
Raising the numerator and the denominator separately to the power indicated
keep the fraction in that form rather than express it as a mixed number
Real Numbers

43. 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.
number of minus signs
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
A root of a number

44. 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
keep the fraction in that form rather than express it as a mixed number
Does not Exist
The operation of raising a number to a power

45. The power of a product is equal to the product obtained when
The number itself
the power is negative
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
a root - the index of which is r.

46. The law of exponents for the power of a product is as follows:
The number of minus signs is odd or even -
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 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.
a root - the index of which is r.

47. 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.
A root
Raising to a power
The inverse of raising a number to a power.

48. Depending on whether the exponent of the base is odd or even.
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 number of minus signs is odd or even -
Add the exponents and raise the common base to the sum of the exponents
A root of a number

49. We recall that the exponent of a number tells
One desired
The number of times that the number is to be taken as a factor
a root - the index of which is r.
Decimal places in the factors together