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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 law of exponents for the power of a product is as follows:
The laws of exponents
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
When the radical symbol is used

2. The law of exponents for multiplication may be stated as follows:
number of minus signs
The inverse 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.
Exponent

3. Is multiplication in which all the numbers being multiplied together are equal.
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.
vinculum
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 to a power

4. The law of exponents for a power of an indicated quotient
a root - the index of which is r.
Real Numbers
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

5. The first power of any number is
One desired
The number itself
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.

6. Depending on whether the exponent of the base is odd or even.
Does not Exist
keep the fraction in that form rather than express it as a mixed number
The number of minus signs is odd or even -
INDEX of the root

7. A fraction is raised to a power by
negative exponents arise
Raising the numerator and the denominator separately to the power indicated
its value is 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.

8. Is a special factor of a number.
a root - the index of which is r.
Decimal places in the factors together
The law of exponents for division may be developed from this example
A root

9. The law of exponents for multiplication may be combined with
The inverse of raising a number to a power.
the rule for fractional exponents to solve problems
The process of finding a root
INDEX of the root

10. The power of a product is equal to the product obtained when
1
the rule for fractional exponents to solve problems
One desired
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

11. When the exponent of a negative number is odd -
the power is negative
The law of exponents for division
1
When the radical symbol is used

12. The square of a real number is
The number of minus signs is odd or even -
a root - the index of which is r.
Positive
Does not Exist

13. Any number divided by itself is
what power is intended and what root is intended
1
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
keep the fraction in that form rather than express it as a mixed number

14. When a radical has no index - the square root is understood to be the
The number itself
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 inverse of raising a number to a power.
One desired

15. In fraction form an exponent shows immediately
Decimal places in the factors together
The process of finding a root
what power is intended and what root is intended
merely moving the expression which contains the exponent to the other position in the fraction

16. Is the inverse of raising a number to a power.
zero power
The process of finding 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.
The power

17. 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.
zero 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.
negative exponents arise
The law of exponents for division may be developed from this example

18. 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 inverse of raising a number to a power.
The number of minus signs is odd or even -
The process of taking a root of a number
The process of finding a root

19. The sign of the product is determined - as in ordinary multiplication - by the
Imaginary Number
The power
number of minus signs
keep the fraction in that form rather than express it as a mixed number

20. It is important to realize that the base must be the same for each factor - in order to apply
The laws of exponents
The number of times that the number is to be taken as a factor
The number itself
1

21. The indicated square root of a negative number is called an
Exponent
Imaginary Number
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.

22. To determine the number of decimal places in the root of a perfect power
Divide the number of decimal places in the radicand by the index of the root.
number of minus signs
1
Real Numbers

23. Positive and negative numbers belong to the class called
merely moving the expression which contains the exponent to the other position in the fraction
The number of minus signs is odd or even -
Real Numbers
Exponent

24. 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 law of exponents for division
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
zero power

25. The laws of exponents for the power of a power may be stated as follows:
number of minus signs
The number of minus signs is odd or even -
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.

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.
negative exponents arise
the rule for fractional exponents to solve problems
Exponent
A root of a number

27. Mark off as many decimal places in the product as there are
When the radical symbol is used
Decimal places in the factors together
A root
negative exponents arise

28. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
INDEX of the root
0 exponent
When the radical symbol is used
negative exponents arise

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
The operation of raising a number to a power
Real Numbers
merely moving the expression which contains the exponent to the other position in the fraction

30. To divide one power into another having the same base
Raising to a power
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 laws of 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.

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

32. The number that indicates the root is called the
negative exponents arise
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
INDEX of the root
Add the exponents and raise the common base to the sum of the exponents

33. 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
A root of a number
When the radical symbol is used
the power is positive

34. To multiply two or more powers having the same base -
Imaginary Number
The law of exponents for division
A root of a number
Add the exponents and raise the common base to the sum of the exponents

35. The line above the number whose root is to be found is a symbol of grouping called the
its value is 1
vinculum
the power is negative
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

36. We recall that the exponent of a number tells
Divide the number of decimal places in the radicand by the index of the root.
One desired
The number of times that the number is to be taken as a factor
what power is intended and what root is intended

37. A fractional exponent of the form 1/r indicates
zero power
When the radical symbol is used
a root - the index of which is r.
INDEX of the root

38. Any number divided by itself results in a _________ and has a value of 1
merely moving the expression which contains the exponent to the other position in the fraction
0 exponent
The 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.

39. When a decimal is raised to a power - the number of decimal places in the result
1
Zero occurs as an exponent
Is equal to the number of places in the decimal multiplied by the exponent.
its value is 1

40. 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.
The process of taking a root of a number
zero power
The law of exponents for division

41. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
The inverse of raising a number to a power.
negative exponents arise
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 law of exponents for division

42. In the answer to a problem such as 4^3 + 4^3.
The law of exponents for division
Zero occurs as an exponent
The number of minus signs is odd or even -
Real Numbers

43. When the exponent is even
number of minus signs
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
the power is positive

44. Finding a root of a number is
Zero occurs as an exponent
vinculum
Divide the number of decimal places in the radicand by the index of the root.
The inverse of raising a number to a power.

45. Is a special case of multiplication in which the factors are all equal.
1
The operation of raising a number to a power
vinculum
the power is negative

46. If an improper fraction occurs in an exponent it is customary to
Raising to a power
keep the fraction in that form rather than express it as a mixed number
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.

47. Is the number of times the number itself is to be taken as a factor.
number of minus signs
The laws of exponents
The power
Divide the number of decimal places in the radicand by the index of the root.

48. Notice that the sign of an exponent may be changed by
A root
Does not Exist
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.

49. When an exponent occurs - it must always be written unless...
Zero occurs as an exponent
The number of times that the number is to be taken as a factor
Divide the number of decimal places in the radicand by the index of the root.
its value is 1