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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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1. 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
The inverse of raising a number to a power.
The law of exponents for division
The number of minus signs is odd or even -

2. 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
vinculum
0 exponent

3. The power of a product is equal to the product obtained when
Zero occurs as an exponent
The law of exponents for division may be developed from this example
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
INDEX of the root

4. The laws of exponents for the power of a power may be stated as follows:
Exponent
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.
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.

5. Any number divided by itself results in a _________ and has a value of 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.
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.
0 exponent

6. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
the rule for fractional exponents to solve problems
When the radical symbol is used
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 is positive

7. 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.
Raising the numerator and the denominator separately to the power indicated
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.
The law of exponents for division may be developed from this example

8. To divide one power into another having the same base
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.
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 laws of exponents
The number of minus signs is odd or even -

9. Mark off as many decimal places in the product as there are
the power is positive
A root
The number of minus signs is odd or even -
Decimal places in the factors together

10. 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 itself
A root of a number
The power
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

11. 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
zero power
One desired
keep the fraction in that form rather than express it as a mixed number

12. The line above the number whose root is to be found is a symbol of grouping called the
vinculum
the power is positive
0 exponent
1

13. Positive and negative numbers belong to the class called
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Real Numbers
One desired
The law of exponents for division may be developed from this example

14. The first power of any number is
The number itself
Real Numbers
The law of exponents for division may be developed from this example
Raising to a power

15. When the exponent is even
the power is positive
its value is 1
A root of a number
The process of taking a root of a number

16. 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 power
Zero occurs as an exponent
Raising to a power
Exponent

17. Is multiplication in which all the numbers being multiplied together are equal.
Raising to a power
The process of finding a root
the power is positive
The number of times that the number is to be taken as a factor

18. When a decimal is raised to a power - the number of decimal places in the result
The number of times that the number is to be taken as a factor
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
Add the exponents and raise the common base to the sum of the exponents

19. When the exponent of a negative number is odd -
the power is negative
number of minus signs
The power
Divide the number of decimal places in the radicand by the index of the root.

20. The sign of the product is determined - as in ordinary multiplication - by the
number of minus signs
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
zero power

21. A fractional exponent of the form 1/r indicates
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.
The number itself
a root - the index of which is r.

22. The square of a real number is
Positive
the rule for fractional exponents to solve problems
The operation of raising a number to a power
Is equal to the number of places in the decimal multiplied by the exponent.

23. Finding a root of a number is
The inverse of raising a number to a power.
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 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.

24. The indicated square root of a negative number is called an
Imaginary Number
Does not Exist
negative exponents arise
Add the exponents and raise the common base to the sum of the exponents

25. It is important to realize that the base must be the same for each factor - in order to apply
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.
Imaginary Number
The laws of exponents
number of minus signs

26. To multiply two or more powers having the same base -
the power is negative
Divide the number of decimal places in the radicand by the index of the root.
The operation of raising a number to a power
Add the exponents and raise the common base to the sum of the exponents

27. Is the inverse of raising a number to a power.
Decimal places in the factors together
The process of finding a root
The inverse of raising a number to a power.
a root - the index of which is r.

28. In the answer to a problem such as 4^3 + 4^3.
a root - the index of which is r.
Divide the number of decimal places in the radicand by the index of the root.
Zero occurs as an exponent
0 exponent

29. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
negative exponents arise
The laws of exponents
Does not Exist
The law of exponents for division

30. Is a special case of multiplication in which the factors are all equal.
The operation of raising a number to a power
a root - the index of which is r.
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.
merely moving the expression which contains the exponent to the other position in the fraction

31. A fraction is raised to a power by
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
Exponent
A root of a number

32. 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.
A root
merely moving the expression which contains the exponent to the other position in the fraction
The law of exponents for division may be developed from this example
The process of taking a root of a number

33. Is the number of times the number itself is to be taken as a factor.
0 exponent
The power
Raising to a power
Divide the number of decimal places in the radicand by the index of the root.

34. When an exponent occurs - it must always be written unless...
Add the exponents and raise the common base to the sum of the exponents
negative exponents arise
A root of a number
its value is 1

35. The law of exponents for multiplication may be stated as follows:
zero power
number of minus signs
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 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.

36. Notice that the sign of an exponent may be changed by
the rule for fractional exponents to solve problems
merely moving the expression which contains the exponent to the other position in the fraction
Does not Exist
A root of a number

37. The law of exponents for a power of an indicated quotient
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.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
A root

38. In fraction form an exponent shows immediately
The law of exponents for division may be developed from this example
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 laws of exponents

39. Is a special factor of a number.
A root of a number
A root
The number of times that the number is to be taken as a factor
Positive

40. Any number (other than zero) raised to the _____ equals 1
a root - the index of which is r.
The law of exponents for division may be developed from this example
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 power

41. We recall that the exponent of a number tells
its value is 1
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
The law of exponents for division

42. 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.
The operation of raising a number to a power
The process of taking a root of a number
Real Numbers

43. Any number divided by itself is
Does not Exist
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.
Positive

44. The law of exponents for multiplication may be combined with
the rule for fractional exponents to solve problems
Is equal to the number of places in the decimal multiplied by the exponent.
The number of times that the number is to be taken as a factor
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.

45. 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
number of minus signs
The law of exponents for division
Divide the number of decimal places in the radicand by the index of the root.

46. The number that indicates the root is called the
Positive
0 exponent
INDEX of the root
what power is intended and what root is intended

47. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
negative exponents arise
Divide the number of decimal places in the radicand by the index of the root.
zero power
The law of exponents for division may be developed from this example

48. Depending on whether the exponent of the base is odd or even.
negative exponents arise
Does not Exist
The number of minus signs is odd or even -
number of minus signs

49. When a radical has no index - the square root is understood to be the
A root of a number
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Raising to a power
One desired

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CLEP General Mathematics: Exponents And Radicals

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