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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 (other than zero) raised to the _____ equals 1
zero power
The operation of raising a number to a power
a root - the index of which is r.
A root

2. Is the number of times the number itself is to be taken as a factor.
One desired
The power
what power is intended and what root is intended
The law of exponents for division may be developed from this example

3. The law of exponents for the power of a product is as follows:
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 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
Decimal places in the factors together

4. The first power of any number is
1
Zero occurs as an exponent
One desired
The number itself

5. To multiply two or more powers having the same base -
its value is 1
Positive
zero power
Add the exponents and raise the common base to the sum of the exponents

6. Is a special case of multiplication in which the factors are all equal.
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.
One desired
The operation of raising a number to a power
Does not Exist

7. When a radical has no index - the square root is understood to be the
One desired
The number itself
0 exponent
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

8. 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 taking a root of a number
The law of exponents for division
A root of a number
Decimal places in the factors together

9. In the answer to a problem such as 4^3 + 4^3.
its value is 1
vinculum
A root of a number
Zero occurs as an exponent

10. 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 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 process of finding a root
The law of exponents for division may be developed from this example
Positive

11. The law of exponents for multiplication may be stated as follows:
The number of minus signs is odd or even -
A root
When the radical symbol is used
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

12. A fractional exponent of the form 1/r indicates
Imaginary Number
The inverse of raising a number to a power.
a root - the index of which is r.
Is equal to the number of places in the decimal multiplied by the exponent.

13. A fraction is raised to a power by
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.
Add the exponents and raise the common base to the sum of the 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.

14. We recall that the exponent of a number tells
The process of taking a root of a number
vinculum
zero power
The number of times that the number is to be taken as a factor

15. The square of a real number is
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.
Exponent
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Positive

16. The law of exponents for multiplication may be combined with
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 process of taking a root of a number
the rule for fractional exponents to solve problems

17. To divide one power into another having the same base
The law of exponents for division may be developed from this example
The process of taking a root of a number
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 the numerator and the denominator separately to the power indicated

18. Any number divided by itself results in a _________ and has a value of 1
Zero occurs as an exponent
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

19. The line above the number whose root is to be found is a symbol of grouping called the
Raising to a 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
vinculum

20. The laws of exponents for the power of a power may be stated as follows:
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 inverse of raising a number to a power.
Divide the number of decimal places in the radicand by the index of the root.

21. Is a special factor of a number.
Real Numbers
the rule for fractional exponents to solve problems
A root
The number of minus signs is odd or even -

22. The sign of the product is determined - as in ordinary multiplication - by the
number of minus signs
The inverse of raising a number to a power.
merely moving the expression which contains the exponent to the other position in the fraction
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.

23. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
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
When the radical symbol is used
negative exponents arise

24. When an exponent occurs - it must always be written unless...
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
its value is 1
The process of taking a root of a number
The laws of exponents

25. The number that indicates the root is called the
the power is positive
zero power
vinculum
INDEX of the root

26. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
The operation of raising a number to a power
The power
Does not Exist
Exponent

27. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
One desired
The inverse 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.
vinculum

28. The law of exponents for a power of an indicated quotient
The law of exponents for division
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 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

29. When a decimal is raised to a power - the number of decimal places in the result
1
Add the exponents and raise the common base to the sum of the exponents
vinculum
Is equal to the number of places in the decimal multiplied by the exponent.

30. Notice that the sign of an exponent may be changed by
The number itself
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 power
merely moving the expression which contains the exponent to the other position in the fraction

31. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
The number of times that the number is to be taken as a factor
When the radical symbol is used
Imaginary Number
The number of minus signs is odd or even -

32. 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 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.
number of minus signs
Exponent

33. In fraction form an exponent shows immediately
number of minus signs
what power is intended and what root is intended
The law of exponents for division may be developed from this example
a root - the index of which is r.

34. It is important to realize that the base must be the same for each factor - in order to apply
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 power
The laws of exponents
Real Numbers

35. If an improper fraction occurs in an exponent it is customary to
The inverse of raising a number to a power.
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
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.

36. 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 number of minus signs is odd or even -
The process of taking a root of a number
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.

37. Any number divided by itself is
The power
vinculum
1
the rule for fractional exponents to solve problems

38. Positive and negative numbers belong to the class called
vinculum
Real Numbers
The power
The process of taking a root of a number

39. To determine the number of decimal places in the root of a perfect 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.
Divide the number of decimal places in the radicand by the index of the root.
Positive
its value is 1

40. The indicated square root of a negative number is called an
1
Imaginary Number
The inverse of raising a number to a power.
keep the fraction in that form rather than express it as a mixed number

41. Depending on whether the exponent of the base is odd or even.
1
The law of exponents for division
The number of minus signs is odd or even -
negative exponents arise

42. Is multiplication in which all the numbers being multiplied together are equal.
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
0 exponent
The process of taking a root of a number

43. When the exponent is even
Decimal places in the factors together
the power is positive
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.

44. When the exponent of a negative number is odd -
INDEX of the root
the power is negative
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.
One desired

45. 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 of a number
The law of exponents for division may be developed from this example
Zero occurs as an exponent
Positive

46. Is the inverse of raising a number to a power.
The process of finding a root
INDEX of the root
The law of exponents for division may be developed from this example
The number of times that the number is to be taken as a factor

47. Finding a root of a number is
The inverse of raising a number to a power.
Real Numbers
The process of finding a root
Divide the number of decimal places in the radicand by the index of the root.

48. Mark off as many decimal places in the product as there are
Decimal places in the factors together
The inverse of raising a number to a power.
number of minus signs
The number itself

49. The power of a product is equal to the product obtained when
a root - the index of which is r.
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.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Imaginary Number