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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. 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.
Is equal to the number of places in the decimal multiplied by the exponent.
INDEX of the root
Zero occurs as an exponent
The law of exponents for division may be developed from this example

2. When the exponent is even
Positive
Decimal places in the factors together
The law of exponents for division
the power is positive

3. Is a special case of multiplication in which the factors are all equal.
Decimal places in the factors together
1
The operation of raising a number to a 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.

4. We recall that the exponent of a number tells
merely moving the expression which contains the exponent to the other position in the fraction
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.
The number of times that the number is to be taken as a factor

5. The laws of exponents for the power of a power may be stated as follows:
The number itself
Is equal to the number of places in the decimal multiplied by the exponent.
negative exponents arise
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.

6. To determine the number of decimal places in the root of a perfect power
The law of exponents for division
Divide the number of decimal places in the radicand by the index of the root.
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

7. When the exponent of a negative number is odd -
Imaginary Number
the power is negative
INDEX of the root
When the radical symbol is used

8. Any number divided by itself is
what power is intended and what root is intended
1
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

9. It is important to realize that the base must be the same for each factor - in order to apply
the power is negative
Is equal to the number of places in the decimal multiplied by the exponent.
The laws of exponents
number of minus signs

10. The first power of any number is
The number itself
the rule for fractional exponents to solve problems
zero power
The number of times that the number is to be taken as a factor

11. Depending on whether the exponent of the base is odd or even.
The process of taking a root of a number
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
0 exponent
The number of minus signs is odd or even -

12. 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.
1
number of minus signs
Add the exponents and raise the common base to the sum of the exponents

13. To multiply two or more powers having the same base -
Raising the numerator and the denominator separately to the power indicated
zero power
Add the exponents and raise the common base to the sum of the exponents
The power

14. The sign of the product is determined - as in ordinary multiplication - by the
merely moving the expression which contains the exponent to the other position in the fraction
number of minus signs
The process of finding a root
Exponent

15. 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.
negative exponents arise
The number itself
A root of a number
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 indicated square root of a negative number is called an
vinculum
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.
number of minus signs
Imaginary Number

17. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
negative exponents arise
zero power
Decimal places in the factors together
The power

18. In the answer to a problem such as 4^3 + 4^3.
Divide the number of decimal places in the radicand by the index of the root.
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
Zero occurs as an exponent

19. The number that indicates the root is called the
Does not Exist
The operation of raising a number to a power
vinculum
INDEX of the root

20. The power of a product is equal to the product obtained when
The process of taking a root of a number
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
its value is 1
Imaginary Number

21. Any number divided by itself results in a _________ and has a value of 1
0 exponent
The power
vinculum
Positive

22. When a decimal is raised to a power - the number of decimal places in the result
INDEX of the root
negative exponents arise
Imaginary Number
Is equal to the number of places in the decimal multiplied by the exponent.

23. When an exponent occurs - it must always be written unless...
Zero occurs as an exponent
Real Numbers
its value is 1
what power is intended and what root is intended

24. Is the number of times the number itself is to be taken as a factor.
Does not Exist
The power
zero power
what power is intended and what root is intended

25. Any number (other than zero) raised to the _____ equals 1
When the radical symbol is used
zero power
Divide the number of decimal places in the radicand by the 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.

26. Is multiplication in which all the numbers being multiplied together are equal.
One desired
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.
Raising to a power
keep the fraction in that form rather than express it as a mixed number

27. A fraction is raised to a power by
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.
number of minus signs
the power is positive
Raising the numerator and the denominator separately to the power indicated

28. 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
The operation of raising a number to a power
Divide the number of decimal places in the radicand by the index of the root.
number of minus signs

29. The line above the number whose root is to be found is a symbol of grouping called the
The law of exponents for division may be developed from this example
keep the fraction in that form rather than express it as a mixed number
Decimal places in the factors together
vinculum

30. Is the inverse of raising a number to a power.
Divide the number of decimal places in the radicand by the index of the root.
The process of finding a root
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
The number of minus signs is odd or even -

31. The law of exponents for a power of an indicated quotient
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.
a root - the index of which is r.
Zero occurs as an 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.
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.
The process of taking a root of a number
The power

33. When a radical has no index - the square root is understood to be the
zero power
The operation of raising a number to a power
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

34. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
Add the exponents and raise the common base to the sum of the exponents
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.
Does not Exist

35. A fractional exponent of the form 1/r indicates
a root - the index of which is r.
When the radical symbol is used
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
INDEX of the root

36. In fraction form an exponent shows immediately
what power is intended and what root is intended
a root - the index of which is r.
The power
1

37. Is a special factor of a number.
Is equal to the number of places in the decimal multiplied by the exponent.
A root
Positive
The operation of raising a number to a power

38. The square of a real number is
The number of times that the number is to be taken as a factor
The inverse of raising a number to a power.
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.

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

40. Finding a root of a number is
The number itself
The inverse of raising a number to a power.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Decimal places in the factors together

41. The law of exponents for multiplication may be combined with
The operation of raising a number to a power
vinculum
its value is 1
the rule for fractional exponents to solve problems

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.
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
When the radical symbol is used
The law of exponents for division
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.

43. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
zero power
When the radical symbol is used
The law of exponents for division
the power is positive

44. The law of exponents for multiplication may be stated as follows:
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.
INDEX of the root
The inverse of raising a number to a power.

45. 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 inverse of raising a number to a power.
Exponent
its value is 1
a root - the index of which is r.

46. The law of exponents for the power of a product is as follows:
Raising to a power
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.
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.

47. Positive and negative numbers belong to the class called
The law of exponents for division may be developed from this example
the rule for fractional exponents to solve problems
Real Numbers
The number of times that the number is to be taken as a factor

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

49. Notice that the sign of an exponent may be changed by
Divide the number of decimal places in the radicand by the index of the root.
merely moving the expression which contains the exponent to the other position in the fraction
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