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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. Any number divided by itself is
1
The operation of raising a number to a power
The laws of exponents
keep the fraction in that form rather than express it as a mixed number

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.
what power is intended and what root is intended
the power is positive
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

3. The law of exponents for a power of an indicated quotient
what power is intended and what root is intended
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 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.
Imaginary Number

4. When a radical has no index - the square root is understood to be the
The law of exponents for division
1
A root
One desired

5. A fractional exponent of the form 1/r indicates
One desired
The laws of exponents
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.

6. Is multiplication in which all the numbers being multiplied together are equal.
Raising to a power
Real Numbers
1
Divide the number of decimal places in the radicand by the index of the root.

7. Positive and negative numbers belong to the class called
the rule for fractional exponents to solve problems
number of minus signs
Real Numbers
negative exponents arise

8. The indicated square root of a negative number is called an
Imaginary Number
vinculum
the rule for fractional exponents to solve problems
merely moving the expression which contains the exponent to the other position in the fraction

9. Any number (other than zero) raised to the _____ equals 1
Is equal to the number of places in the decimal multiplied by the exponent.
zero 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.
A root of a number

10. 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.
negative exponents arise
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.

11. The line above the number whose root is to be found is a symbol of grouping called the
vinculum
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
The number itself
merely moving the expression which contains the exponent to the other position in the fraction

12. Any number divided by itself results in a _________ and has a value of 1
0 exponent
the power is positive
A root of a number
INDEX of the root

13. Is the number of times the number itself is to be taken as a factor.
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
The laws of exponents
The process of finding a root

14. The square of a real number is
Is equal to the number of places in the decimal multiplied by the exponent.
Positive
The laws of exponents
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

15. The power of a product is equal to the product obtained when
INDEX of the root
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Does not Exist
Zero occurs as an exponent

16. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
The number of times that the number is to be taken as a factor
Zero occurs as an exponent
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.
Is equal to the number of places in the decimal multiplied by the exponent.

17. The number that indicates the root is called the
the rule for fractional exponents to solve problems
INDEX of the root
0 exponent
Decimal places in the factors together

18. 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.
Exponent
keep the fraction in that form rather than express it as a mixed number
The number itself
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. In the answer to a problem such as 4^3 + 4^3.
negative exponents arise
When the radical symbol is used
Zero occurs as an exponent
Raising the numerator and the denominator separately to the power indicated

20. 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.
INDEX of the root
Zero occurs as an exponent
The law of exponents for division
keep the fraction in that form rather than express it as a mixed number

21. 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
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
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.

22. Mark off as many decimal places in the product as there are
keep the fraction in that form rather than express it as a mixed number
its value is 1
the power is positive
Decimal places in the factors together

23. When a decimal is raised to a power - the number of decimal places in the result
The laws of exponents
Is equal to the number of places in the decimal multiplied by the exponent.
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

24. In fraction form an exponent shows immediately
0 exponent
The operation of raising a number to a power
Add the exponents and raise the common base to the sum of the exponents
what power is intended and what root is intended

25. If an improper fraction occurs in an exponent it is customary to
1
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
keep the fraction in that form rather than express it as a mixed number
Divide the number of decimal places in the radicand by the index of the root.

26. When the exponent of a negative number is odd -
The laws of exponents
Divide the number of decimal places in the radicand by the index of the root.
the power is negative
The process of finding a root

27. Is a special case of multiplication in which the factors are all equal.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Decimal places in the factors together
The operation of raising a number to a power
negative exponents arise

28. Notice that the sign of an exponent may be changed by
The number itself
merely moving the expression which contains the exponent to the other position in the fraction
the power is positive
The number of times that the number is to be taken as a factor

29. The sign of the product is determined - as in ordinary multiplication - by the
vinculum
its value is 1
keep the fraction in that form rather than express it as a mixed number
number of minus signs

30. Is a special factor of a number.
zero power
A root
The number itself
The power

31. When an exponent occurs - it must always be written unless...
The law of exponents for division may be developed from this example
Imaginary Number
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.

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.
The process of taking a root of a number
The number of times that the number is to be taken as a factor
0 exponent
A root of a number

33. Finding a root of a number is
One desired
The inverse of raising a number to a power.
The operation of raising a number to a power
0 exponent

34. We recall that the exponent of a number tells
The process of finding a root
The number of times that the number is to be taken as a factor
what power is intended and what root is intended
The operation of raising a number to a power

35. Depending on whether the exponent of the base is odd or even.
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 inverse of raising a number to a power.
The number of minus signs is odd or even -

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
the power is negative
The inverse of raising a number to a 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.

37. When the exponent is even
Positive
the power is positive
A root of a number
Zero occurs as an exponent

38. The law of exponents for the power of a product is as follows:
the rule for fractional exponents to solve problems
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.
The power

39. The first power of any number is
The number itself
Positive
0 exponent
Decimal places in the factors together

40. To divide one power into another having the same base
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.
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 value is 1
Zero occurs as an exponent

41. The laws of exponents for the power of a power may be stated as follows:
the power is positive
Raising 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.
keep the fraction in that form rather than express it as a mixed number

42. 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 law of exponents for division may be developed from this example
The operation of raising a number to a power
When the radical symbol is used
A root of a number

43. Is the inverse of raising a number to a power.
The process of finding a root
Imaginary Number
number of minus signs
Zero occurs as an exponent

44. It is important to realize that the base must be the same for each factor - in order to apply
Positive
zero power
The laws of exponents
The number itself

45. The law of exponents for multiplication may be combined with
The number of minus signs is odd or even -
the rule for fractional exponents to solve problems
Is equal to the number of places in the decimal multiplied by the exponent.
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.

46. A fraction is raised to a power by
Raising the numerator and the denominator separately to the power indicated
Divide the number of decimal places in the radicand by the index of the 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.
Zero occurs as an exponent

47. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
The number of minus signs is odd or even -
The law of exponents for division
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.
negative exponents arise

48. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
The process of taking a root of a number
When the radical symbol is used
0 exponent
the power is negative

49. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
zero power
Real Numbers
Does not Exist
a root - the index of which is r.