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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. The law of exponents for multiplication may be stated as follows:
number of minus signs
The law of exponents for division
Does not Exist
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

2. 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.
One desired
the power is positive
a root - the index of which is r.
The process of taking a root of a number

3. Is the number of times the number itself is to be taken as a factor.
the power is negative
Add the exponents and raise the common base to the sum of the exponents
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

4. Is a special case of multiplication in which the factors are all equal.
the rule for fractional exponents to solve problems
The law of exponents for division may be developed from this example
the power is negative
The operation of raising a number to a power

5. 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 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 negative
Does not Exist
merely moving the expression which contains the exponent to the other position in the fraction

6. The sign of the product is determined - as in ordinary multiplication - by the
INDEX of the 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

7. When a decimal is raised to a power - the number of decimal places in the result
Is equal to the number of places in the decimal multiplied by the exponent.
number of minus signs
Positive
what power is intended and what root is intended

8. We recall that the exponent of a number tells
zero power
Is equal to the number of places in the decimal multiplied by the exponent.
Divide the number of decimal places in the radicand by the index of the root.
The number of times that the number is to be taken as a factor

9. To multiply two or more powers having the same base -
0 exponent
what power is intended and what root is intended
Add the exponents and raise the common base to the sum of the exponents
Decimal places in the factors together

10. The first power of any number is
A root of a number
merely moving the expression which contains the exponent to the other position in the fraction
1
The number itself

11. When the exponent is even
the power is positive
The laws of exponents
Decimal places in the factors together
keep the fraction in that form rather than express it as a mixed number

12. To divide one power into another having the same base
The inverse of raising a number to a power.
0 exponent
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

13. 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
The number of minus signs is odd or even -
The law of exponents for division may be developed from this example
negative exponents arise

14. A fraction is raised to a power by
The number itself
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.
The power

15. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
number of minus signs
The process of finding a root
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.
One desired

16. 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.
Zero occurs as an exponent
A root of a number
the rule for fractional exponents to solve problems
merely moving the expression which contains the exponent to the other position in the fraction

17. Depending on whether the exponent of the base is odd or even.
merely moving the expression which contains the exponent to the other position in the fraction
The number of minus signs is odd or even -
the power is negative
Is equal to the number of places in the decimal multiplied by the exponent.

18. When an exponent occurs - it must always be written unless...
its value is 1
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 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 is negative

19. When a radical has no index - the square root is understood to be the
Divide the number of decimal places in the radicand by the index of the root.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
One desired
its value is 1

20. The laws of exponents for the power of a power may be stated as follows:
0 exponent
Raising the numerator and the denominator separately to the power indicated
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.

21. When the exponent of a negative number is odd -
its value is 1
vinculum
the power is negative
Raising the numerator and the denominator separately to the power indicated

22. Is a special factor of a number.
A root
The inverse of raising a number to a power.
A root of a number
Does not Exist

23. 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 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
zero power

24. Is the inverse of raising a number to a power.
number of minus signs
the power 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.
The process of finding a root

25. The square of a real number is
vinculum
keep the fraction in that form rather than express it as a mixed number
Positive
the power is negative

26. Any number divided by itself is
1
Decimal places in the factors together
zero power
the power is positive

27. The law of exponents for the power of a product is as follows:
Zero occurs as an exponent
Divide the number of decimal places in the radicand by the index of the root.
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 rule for fractional exponents to solve problems

28. Notice that the sign of an exponent may be changed by
the power is positive
The laws of exponents
merely moving the expression which contains the exponent to the other position in the fraction
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.

29. 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.
The law of exponents for division
Decimal places in the factors together
Divide the number of decimal places in the radicand by the index of the root.
merely moving the expression which contains the exponent to the other position in the fraction

30. The line above the number whose root is to be found is a symbol of grouping called the
vinculum
zero power
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.

31. Any number divided by itself results in a _________ and has a value of 1
0 exponent
a root - the index of which is r.
Zero occurs as an exponent
The number of times that the number is to be taken as a factor

32. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
negative exponents arise
Exponent
The law of exponents for division may be developed from this example
Zero occurs as an exponent

33. Any number (other than zero) raised to the _____ equals 1
A root
merely moving the expression which contains the exponent to the other position in the fraction
zero power
what power is intended and what root is intended

34. The law of exponents for multiplication may be combined with
Divide the number of decimal places in the radicand by the index of the root.
negative exponents arise
Raising the numerator and the denominator separately to the power indicated
the rule for fractional exponents to solve problems

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

36. Is multiplication in which all the numbers being multiplied together are equal.
Raising to a power
The number itself
number of minus signs
Positive

37. Positive and negative numbers belong to the class called
0 exponent
Does not Exist
The operation of raising a number to a power
Real Numbers

38. The law of exponents for a power of an indicated quotient
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.
The number of minus signs is odd or even -
The inverse of raising a number to a power.

39. The indicated square root of a negative number is called an
Imaginary Number
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.
its value is 1

40. Mark off as many decimal places in the product as there are
When the radical symbol is used
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.
Decimal places in the factors together

41. The number that indicates the root is called the
the rule for fractional exponents to solve problems
The laws of exponents
The process of finding a root
INDEX of the root

42. In fraction form an exponent shows immediately
Decimal places in the factors together
Exponent
what power is intended and what root is intended
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

43. Finding a root of a number is
The inverse of raising a number to a power.
the power is negative
Raising to a power
the power is positive

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

45. If an improper fraction occurs in an exponent it is customary to
vinculum
The process of taking a root of a number
keep the fraction in that form rather than express it as a mixed 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.

46. To determine the number of decimal places in the root of a perfect power
its value is 1
When the radical symbol is used
The law of exponents for division may be developed from this example
Divide the number of decimal places in the radicand by the index of the root.

47. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
Add the exponents and raise the common base to the sum of the exponents
The process of finding a root
The inverse of raising a number to a power.
When the radical symbol is used

48. 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.
0 exponent
Exponent
Real Numbers
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.

49. It is important to realize that the base must be the same for each factor - in order to apply
The operation of raising a number to a power
The laws of exponents
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 is negative