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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 sign of the product is determined - as in ordinary multiplication - by the
Divide the number of decimal places in the radicand by the index of the root.
the rule for fractional exponents to solve problems
number of minus signs
The number of minus signs is odd or even -

2. A fractional exponent of the form 1/r indicates
keep the fraction in that form rather than express it as a mixed number
a root - the index of which is r.
vinculum
A root of a number

3. When a decimal is raised to a power - the number of decimal places in the result
its value is 1
the rule for fractional exponents to solve problems
Is equal to the number of places in the decimal multiplied by the exponent.
A root of a number

4. The laws of exponents for the power of a power may be stated as follows:
The number itself
INDEX of the root
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.

5. The indicated square root of a negative number is called an
The law of exponents for division
INDEX of the root
0 exponent
Imaginary Number

6. Notice that the sign of an exponent may be changed by
The inverse of raising a number to a power.
The number of times that the number is to be taken as a factor
The law of exponents for division
merely moving the expression which contains the exponent to the other position in the fraction

7. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
Real Numbers
negative exponents arise
Imaginary Number
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

8. When the exponent is even
keep the fraction in that form rather than express it as a mixed number
the power is positive
The number of times that the number is to be taken as a factor
merely moving the expression which contains the exponent to the other position in the fraction

9. 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.
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
Raising to a power
The law of exponents for division may be developed from this example
negative exponents arise

10. 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.
Raising to a power
Real Numbers
The law of exponents for division
the power is positive

11. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
Does not Exist
Zero occurs as an exponent
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.

12. The number that indicates the root is called the
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.
INDEX of the root
Raising to a power
The process of taking a root of a number

13. Is a special case of multiplication in which the factors are all equal.
The operation of raising a number to a power
The number of minus signs is odd or even -
Raising the numerator and the denominator separately to the power indicated
One desired

14. Finding a root of a number is
the rule for fractional exponents to solve problems
keep the fraction in that form rather than express it as a mixed number
The number itself
The inverse of raising a number to a power.

15. Is a special factor 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.
A root
negative exponents arise
the power is negative

16. Mark off as many decimal places in the product as there are
The process of taking a root of a number
The law of exponents for division
its value is 1
Decimal places in the factors together

17. When an exponent occurs - it must always be written unless...
its value is 1
The process of finding a root
Positive
Does not Exist

18. The power of a product is equal to the product obtained when
The law of exponents for division
number of minus signs
A root of a number
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

19. 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.
1
The number of minus signs is odd or even -
0 exponent
The process of taking a root of a number

20. In the answer to a problem such as 4^3 + 4^3.
negative exponents arise
A root of a number
Zero occurs as an exponent
what power is intended and what root is intended

21. 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.
keep the fraction in that form rather than express it as a mixed number
vinculum
Exponent
Divide the number of decimal places in the radicand by the index of the root.

22. Any number (other than zero) raised to the _____ equals 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.
zero power
The process of taking a root of a number
The number of minus signs is odd or even -

23. Is the number of times the number itself is to be taken as a factor.
1
Does not Exist
The power
Decimal places in the factors together

24. Is multiplication in which all the numbers being multiplied together are equal.
merely moving the expression which contains the exponent to the other position in the fraction
keep the fraction in that form rather than express it as a mixed number
When the radical symbol is used
Raising to a power

25. The first power of any number is
The operation of raising a number to a power
The number itself
Imaginary Number
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

26. When a radical has no index - the square root is understood to be the
The laws of exponents
One desired
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

27. The law of exponents for multiplication may be combined with
the rule for fractional exponents to solve problems
Zero occurs as an 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 number itself

28. The law of exponents for a power of an indicated 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.
The law of exponents for division may be developed from this example
One desired
The inverse of raising a number to a power.

29. 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 law of exponents for division
The number itself
The laws of exponents

30. Any number divided by itself 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.
A root of a number
Add the exponents and raise the common base to the sum of the exponents

31. To determine the number of decimal places in the root of a perfect power
A root of a number
what power is intended and what root is intended
Divide the number of decimal places in the radicand by the index of the root.
number of minus signs

32. A fraction is raised to a power by
Raising the numerator and the denominator separately to the power indicated
The number of minus signs is odd or even -
When the radical symbol is used
Divide the number of decimal places in the radicand by the index of the root.

33. To divide one power into another having the same base
a root - the index of which is r.
Real Numbers
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.

34. Any number divided by itself results in a _________ and has a value of 1
0 exponent
The inverse of raising a number to a power.
merely moving the expression which contains the exponent to the other position in the fraction
The process of taking a root of a number

35. When the exponent of a negative number is odd -
Zero occurs as an exponent
Real Numbers
the power is negative
Add the exponents and raise the common base to the sum of the exponents

36. The line above the number whose root is to be found is a symbol of grouping called the
The number of minus signs is odd or even -
Raising the numerator and the denominator separately to the power indicated
vinculum
The operation of raising a number to a power

37. 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
When the radical symbol is used
The power
negative exponents arise

38. Is the inverse of raising a number to a power.
The law of exponents for division may be developed from this example
negative exponents arise
The process of finding a root
Real Numbers

39. The law of exponents for the power of a product is as follows:
The number itself
The process of taking a root of a number
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.

40. The law of exponents for multiplication may be stated as follows:
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
Divide the number of decimal places in the radicand by the index of the root.
0 exponent
number of minus signs

41. We recall that the exponent of a number tells
INDEX of the root
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.
Does not Exist

42. 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
1
Zero occurs as an exponent
The power

43. It is important to realize that the base must be the same for each factor - in order to apply
The laws of exponents
negative exponents arise
Zero occurs as an exponent
When the radical symbol is used

44. 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.
number of minus signs
Raising the numerator and the denominator separately to the power indicated
a root - the index of which is r.
A root of a number

45. Positive and negative numbers belong to the class called
Real Numbers
a root - the index of which is r.
Is equal to the number of places in the decimal multiplied by the exponent.
merely moving the expression which contains the exponent to the other position in the fraction

46. Depending on whether the exponent of the base is odd or even.
INDEX of the root
The number of minus signs is odd or even -
One desired
A root

47. The square of a real number is
The process of taking a root of a number
Positive
One desired
The power

48. In fraction form an exponent shows immediately
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.
what power is intended and what root is intended
The law of exponents for division may be developed from this example

49. To multiply two or more powers having the same base -
Add the exponents and raise the common base to the sum of the exponents
Zero occurs as an exponent
keep the fraction in that form rather than express it as a mixed number
Decimal places in the factors together