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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. Is a special case of multiplication in which the factors are all equal.
The number itself
The operation of raising a number to a power
One desired
The power

2. The first power of any number is
The law of exponents for division
Positive
The number itself
A root

3. To multiply two or more powers having the same base -
The law of exponents for division
keep the fraction in that form rather than express it as a mixed number
The number of minus signs is odd or even -
Add the exponents and raise the common base to the sum of the exponents

4. A fraction is raised to a power by
The process of taking a root of a number
Raising the numerator and the denominator separately to the power indicated
the rule for fractional exponents to solve problems
Does not Exist

5. When the exponent of a negative number is odd -
The law of exponents for division
the power is negative
INDEX of the root
The number of times that the number is to be taken as a factor

6. The law of exponents for a power of an indicated quotient
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 rule for fractional exponents to solve problems
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 power is negative

7. Is the inverse of raising a number to a power.
Is equal to the number of places in the decimal multiplied by the exponent.
The laws of exponents
The process of finding a root
Raising to a power

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

9. Any number divided by itself results in a _________ and has a value of 1
A root
0 exponent
a root - the index of which is r.
One desired

10. When an exponent occurs - it must always be written unless...
a root - the index of which is r.
zero power
the power is negative
its value is 1

11. Finding a root of a number is
The inverse of raising a number to a power.
The operation of raising a number to a power
One desired
The number itself

12. The square of a real number is
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.
Real Numbers
Does not Exist
Positive

13. 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.
Exponent
Divide the number of decimal places in the radicand by the index of the root.
A root of a number

14. Is multiplication in which all the numbers being multiplied together are equal.
A root
vinculum
a root - the index of which is r.
Raising to a power

15. When a radical has no index - the square root is understood to be the
merely moving the expression which contains the exponent to the other position in the fraction
One desired
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
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.

16. 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.
The operation of raising a number to a power
negative exponents arise
The law of exponents for division may be developed from this example

17. We recall that the exponent of a number tells
what power is intended and what root is intended
Add the exponents and raise the common base to the sum of the exponents
Imaginary Number
The number of times that the number is to be taken as a factor

18. 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
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
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.

19. The line above the number whose root is to be found is a symbol of grouping called the
negative exponents arise
The number itself
A root of a number
vinculum

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.
The number of minus signs is odd or even -
Raising the numerator and the denominator separately to the power indicated
The law of exponents for division
Imaginary Number

21. The number that indicates the root is called the
1
The process of finding a root
INDEX of the root
The operation of raising a number to a power

22. 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 process of finding a root
A root of a number
One desired

23. 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.
negative exponents arise
INDEX of the root
The number of times that the number is to be taken as a factor

24. When the exponent is even
A root
the power is positive
what power is intended and what root is intended
The process of taking a root of a number

25. Any number (other than zero) raised to the _____ equals 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.
When the radical symbol is used
Add the exponents and raise the common base to the sum of the exponents
zero power

26. 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.
A root of a number
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.
keep the fraction in that form rather than express it as a mixed number

27. Is the number of times the number itself is to be taken as a factor.
Raising to a power
The power
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.

28. Mark off as many decimal places in the product as there are
The power
Decimal places in the factors together
negative exponents arise
merely moving the expression which contains the exponent to the other position in the fraction

29. If an improper fraction occurs in an exponent it is customary to
The power
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
keep the fraction in that form rather than express it as a mixed number
The process of finding a root

30. 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.
Positive
Real Numbers
The process of taking a root of a number
Decimal places in the factors together

31. 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.
Exponent
The number of times that the number is to be taken as a factor
1
A root of a number

32. In the answer to a problem such as 4^3 + 4^3.
The power
Zero occurs as an 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.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

33. Any number divided by itself is
1
Is equal to the number of places in the decimal multiplied by the exponent.
The number itself
The process of finding a root

34. Is a special factor of a number.
The process of finding a root
a root - the index of which is r.
the power is negative
A root

35. It is important to realize that the base must be the same for each factor - in order to apply
The laws of exponents
1
Positive
The number itself

36. 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 -
Real Numbers
negative exponents arise
number of minus signs

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

38. Positive and negative numbers belong to the class called
what power is intended and what root is intended
Add the exponents and raise the common base to the sum of the exponents
Real Numbers
The number of minus signs is odd or even -

39. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
The operation of raising a number 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.
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

40. Depending on whether the exponent of the base is odd or even.
The number of times that the number is to be taken as a factor
The law of exponents for division may be developed from this example
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 number of minus signs is odd or even -

41. To determine the number of decimal places in the root of a perfect power
A root of a number
The power
Divide the number of decimal places in the radicand by the index of the root.
The process of taking a root of a number

42. The power of a product is equal to the product obtained when
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.
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
its value is 1

43. In fraction form an exponent shows immediately
Raising the numerator and the denominator separately to the power indicated
The operation of raising a number to a power
what power is intended and what root is intended
0 exponent

44. 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.
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
Raising the numerator and the denominator separately to the power indicated
The law of exponents for division may be developed from this example

45. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
Does not Exist
When the radical symbol is used
A root
the power is negative

46. The indicated square root of a negative number is called an
Imaginary Number
merely moving the expression which contains the exponent to the other position in the fraction
the power is positive
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

47. Notice that the sign of an exponent may be changed by
A root
merely moving the expression which contains the exponent to the other position in the fraction
Is equal to the number of places in the decimal multiplied by the exponent.
A root of a number

48. The laws of exponents for the power of a power may be stated as follows:
The number of times that the number is to be taken as a factor
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 inverse of raising a number to a power.
The number itself

49. The sign of the product is determined - as in ordinary multiplication - by the
The number of times that the number is to be taken as a factor
number of minus signs
negative exponents arise
INDEX of the root