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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 first power of any number is
The process of taking a root of a number
The law of exponents for division may be developed from this example
The number itself
The law of exponents for division

2. The power of a product is equal to the product obtained when
The power
The process of taking a root of a number
Decimal places in the factors together
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

3. 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
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
Does not Exist

4. A fraction is raised to a power by
When the radical symbol is used
Raising the numerator and the denominator separately to the power indicated
the power is positive
The inverse of raising a number to a power.

5. 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.
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
A root of a number
what power is intended and what root is intended
Imaginary Number

6. Is a special case of multiplication in which the factors are all equal.
The process of taking a root of a number
The operation of raising a number to a power
the power is negative
INDEX of the root

7. Any number divided by itself results in a _________ and has a value of 1
A root of a number
0 exponent
a root - the index of which is r.
Raising to a power

8. The laws of exponents for the power of a power may be stated as follows:
When the radical symbol is used
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 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.

9. We recall that the exponent of a number tells
Exponent
Positive
The number of times that the number is to be taken as a factor
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.

10. It is important to realize that the base must be the same for each factor - in order to apply
the power is positive
Add the exponents and raise the common base to the sum of the exponents
zero power
The laws of exponents

11. Positive and negative numbers belong to the class called
Is equal to the number of places in the decimal multiplied by the exponent.
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
Real Numbers
number of minus signs

12. The sign of the product is determined - as in ordinary multiplication - by the
number of minus signs
what power is intended and what root is intended
Decimal places in the factors together
the power is negative

13. In the answer to a problem such as 4^3 + 4^3.
Raising to a power
negative exponents arise
Zero occurs as an exponent
Real Numbers

14. To determine the number of decimal places in the root of a perfect power
Does not Exist
Divide the number of decimal places in the radicand by the index of the root.
0 exponent
what power is intended and what root is intended

15. To multiply two or more powers having the same base -
vinculum
Add the exponents and raise the common base to the sum of the exponents
The law of exponents for division
its value is 1

16. Any number (other than zero) raised to the _____ equals 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.
zero power
the power is negative
Raising the numerator and the denominator separately to the power indicated

17. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
When the radical symbol is used
One desired
A root of a number

18. Is a special factor of a number.
1
A root
The number of minus signs is odd or even -
Divide the number of decimal places in the radicand by the index of the root.

19. If an improper fraction occurs in an exponent it is customary to
The number of times that the number is to be taken as a factor
a root - the index of which is r.
the power is negative
keep the fraction in that form rather than express it as a mixed number

20. Notice that the sign of an exponent may be changed by
merely moving the expression which contains the exponent to the other position in the fraction
The power
what power is intended and what root is intended
Add the exponents and raise the common base to the sum of the exponents

21. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
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.
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

22. Is multiplication in which all the numbers being multiplied together are equal.
Does not Exist
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.
Raising to a power

23. 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.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Decimal places in the factors together
negative exponents arise

24. The law of exponents for multiplication may be combined with
1
The power
the rule for fractional exponents to solve problems
Real Numbers

25. Any number divided by itself is
Divide the number of decimal places in the radicand by the index of the root.
Positive
Imaginary Number
1

26. In fraction form an exponent shows immediately
merely moving the expression which contains the exponent to the other position in the fraction
what power is intended and what root is intended
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 the numerator and the denominator separately to the power indicated

27. When the exponent of a negative number is odd -
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 times that the number is to be taken as a factor
Raising the numerator and the denominator separately to the power indicated
the power is negative

28. 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 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.
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.

29. 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
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.
a root - the index of which is r.
zero power

30. The indicated square root of a negative number is called an
A root of a number
Imaginary 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 process of taking a root of a number

31. When a decimal is raised to a power - the number of decimal places in the result
INDEX of the root
Is equal to the number of places in the decimal multiplied by the exponent.
The operation of raising a number to a power
Zero occurs as an exponent

32. The line above the number whose root is to be found is a symbol of grouping called the
The process of taking a root of a number
negative exponents arise
Zero occurs as an exponent
vinculum

33. 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
Positive
The power
a root - the index of which is r.

34. The number that indicates the root is called the
what power is intended and what root is intended
keep the fraction in that form rather than express it as a mixed number
INDEX of the root
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.

35. 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.
Does not Exist
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.

36. A fractional exponent of the form 1/r indicates
When the radical symbol is used
The operation of raising a number to a power
a root - the index of which is r.
Does not Exist

37. Is the number of times the number itself is to be taken as a factor.
the power is positive
a root - the index of which is r.
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

38. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
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.
negative exponents arise
Divide the number of decimal places in the radicand by the index of the root.

39. Depending on whether the exponent of the base is odd or even.
number of minus signs
0 exponent
the rule for fractional exponents to solve problems
The number of minus signs is odd or even -

40. When a radical has no index - the square root is understood to be the
The number of times that the number 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.
One desired
the rule for fractional exponents to solve problems

41. When the exponent is even
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
the power is positive
Add the exponents and raise the common base to the sum of the exponents

42. 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.
what power is intended and what root is intended
The law of exponents for division
Divide the number of decimal places in the radicand by the index of the root.
the rule for fractional exponents to solve problems

43. Is the inverse of raising a number to a power.
The process of finding a root
merely moving the expression which contains the exponent to the other position in the fraction
The number of times that the number is to be taken as a factor
zero power

44. Mark off as many decimal places in the product as there are
Decimal places in the factors together
The number itself
Raising the numerator and the denominator separately to the power indicated
Exponent

45. 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.
Real Numbers
The process of taking a root of a number
The number of minus signs is odd or even -
Raising to a power

46. The law of exponents for multiplication may be stated as follows:
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.
The inverse of raising a number 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.

47. The square of a real number is
Positive
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.
A root

48. When an exponent occurs - it must always be written unless...
Is equal to the number of places in the decimal multiplied by the 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.
its value is 1
merely moving the expression which contains the exponent to the other position in the fraction

49. Finding a root of a number is
Divide the number of decimal places in the radicand by the index of the root.
keep the fraction in that form rather than express it as a mixed number
The inverse of raising a number to a power.
the rule for fractional exponents to solve problems