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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 number that indicates the root is called the
The law of exponents for division may be developed from this example
what power is intended and what root is intended
INDEX of the root
Is equal to the number of places in the decimal multiplied by the exponent.

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

3. The square of a real number is
Positive
One desired
Decimal places in the factors together
A root

4. 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 number itself
Is equal to the number of places in the decimal multiplied by the exponent.
the power is negative

5. Is multiplication in which all the numbers being multiplied together are equal.
The process of taking a root of a number
the rule for fractional exponents to solve problems
Raising to a power
The inverse of raising a number to a power.

6. When the exponent of a negative number is odd -
the rule for fractional exponents to solve problems
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
the power is negative
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.

7. 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.
When the radical symbol is used
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.
Is equal to the number of places in the decimal multiplied by the exponent.

8. Depending on whether the exponent of the base is odd or even.
The number of minus signs is odd or even -
the rule for fractional exponents to solve problems
1
what power is intended and what root is intended

9. When the exponent is even
0 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 positive
A root of a number

10. When an exponent occurs - it must always be written unless...
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
its value is 1
The power
Divide the number of decimal places in the radicand by the index of the root.

11. Any number (other than zero) raised to the _____ equals 1
zero power
negative exponents arise
Raising to a power
The number itself

12. Any number divided by itself results in a _________ and has a value of 1
The process of taking a root of a 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 process of finding a root
0 exponent

13. 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
The power
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

14. Finding a root of a 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.
Zero occurs as an exponent
Positive
The inverse of raising a number to a power.

15. We recall that the exponent of a number tells
The number of times that the number is to be taken as a factor
Real Numbers
The process of taking a root of a 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.

16. 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 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 inverse of raising a number to a power.

17. In the answer to a problem such as 4^3 + 4^3.
Is equal to the number of places in the decimal multiplied by the exponent.
Zero occurs as an exponent
The number of times that the number is to be taken as a factor
Divide the number of decimal places in the radicand by the index of the root.

18. 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.
vinculum
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
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.

19. 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.
the rule for fractional exponents to solve problems
vinculum
The law of exponents for division may be developed from this example

20. The line above the number whose root is to be found is a symbol of grouping called the
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
vinculum
Does not Exist

21. The law of exponents for multiplication may be stated as follows:
Positive
When the radical symbol is used
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.

22. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
Raising the numerator and the denominator separately to the power indicated
negative exponents arise
Positive
The law of exponents for division

23. In fraction form an exponent shows immediately
The number of times that the number is to be taken as a factor
what power is intended and what root is intended
its value is 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.

24. Mark off as many decimal places in the product as there are
Decimal places in the factors together
its value is 1
Zero occurs as an exponent
A root of a number

25. To divide one power into another having the same base
1
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.
Does not Exist
When the radical symbol is used

26. Is a special case of multiplication in which the factors are all equal.
Real Numbers
a root - the index of which is r.
The operation of raising a number to a power
One desired

27. Positive and negative numbers belong to the class called
Real Numbers
its value is 1
Raising to a power
merely moving the expression which contains the exponent to the other position in the fraction

28. Is a special factor of a number.
1
A root
the rule for fractional exponents to solve problems
INDEX of the root

29. The law of exponents for multiplication may be combined with
the rule for fractional exponents to solve problems
merely moving the expression which contains the exponent to the other position in the fraction
The laws of 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.

30. Notice that the sign of an exponent may be changed by
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.
Add the exponents and raise the common base to the sum of the exponents
merely moving the expression which contains the exponent to the other position in the fraction

31. Is the inverse of raising a number to a power.
The inverse of raising a number to a power.
The process of finding a 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.
what power is intended and what root is intended

32. A fraction is raised to a power by
INDEX of the root
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
Raising the numerator and the denominator separately to the power indicated

33. The power of a product is equal to the product obtained when
When the radical symbol is used
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
negative exponents arise
Imaginary Number

34. 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.
A root
A root of a 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 number of times that the number is to be taken as a factor

35. 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
Real Numbers
vinculum
The power

36. To multiply two or more powers having the same base -
Add the exponents and raise the common base to the sum of the exponents
Does not Exist
its value is 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.

37. It is important to realize that the base must be the same for each factor - in order to apply
When the radical symbol is used
0 exponent
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.

38. 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.
A root of a number
The number itself

39. Is the number of times the number itself is to be taken as a factor.
keep the fraction in that form rather than express it as a mixed number
1
The power
The law of exponents for division

40. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
vinculum
The number of minus signs is odd or even -
Does not Exist
the rule for fractional exponents to solve problems

41. The law of exponents for a power of an indicated 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.
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.
Raising to a power

42. 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 inverse of raising a number to a power.
Exponent
Raising the numerator and the denominator separately to the power indicated
0 exponent

43. The first power of any number is
The law of exponents for division
The process of finding a root
The process of taking a root of a number
The number itself

44. When a radical has no index - the square root is understood to be the
Real Numbers
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
One desired

45. The sign of the product is determined - as in ordinary multiplication - by the
Real Numbers
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
number of minus signs
Raising the numerator and the denominator separately to the power indicated

46. A fractional exponent of the form 1/r indicates
Positive
0 exponent
the rule for fractional exponents to solve problems
a root - the index of which is r.

47. Any number divided by itself is
number of minus signs
1
the power is negative
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.

48. The indicated square root of a negative number is called an
Real Numbers
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Imaginary Number
Add the exponents and raise the common base to the sum of the exponents

49. 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.
the power is negative
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