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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. In fraction form an exponent shows immediately
The inverse of raising a number to a power.
what power is intended and what root is intended
Zero occurs as an exponent
The law of exponents for division

2. Positive and negative numbers belong to the class called
The law of exponents for division may be developed from this example
0 exponent
Add the exponents and raise the common base to the sum of the exponents
Real Numbers

3. The number that indicates the root is called the
The inverse of raising a number to a power.
its value is 1
A root of a number
INDEX of the root

4. Is multiplication in which all the numbers being multiplied together are equal.
what power is intended and what root is intended
Zero occurs as an exponent
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

5. Is the number of times the number itself is to be taken as a factor.
The power
Real Numbers
A root of a number
a root - the index of which is r.

6. It is important to realize that the base must be the same for each factor - in order to apply
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.
the rule for fractional exponents to solve problems
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.

7. Is a special factor of a 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 power is positive
Exponent
A root

8. 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
One desired
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.

9. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
Raising to a power
0 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.
A root

10. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
When the radical symbol is used
what power is intended and what root is intended
The number of minus signs is odd or even -
Add the exponents and raise the common base to the sum of the exponents

11. If an improper fraction occurs in an exponent it is customary to
0 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.
keep the fraction in that form rather than express it as a mixed 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.

12. When the exponent is even
the power is positive
The power
Raising the numerator and the denominator separately to the power indicated
Positive

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

14. 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.
Positive
negative exponents arise
One desired

15. The first power of any number is
what power is intended and what root is intended
A root of a number
The number itself
The process of taking a root of a number

16. The law of exponents for multiplication may be combined with
keep the fraction in that form rather than express it as a mixed number
Is equal to the number of places in the decimal multiplied by the exponent.
the rule for fractional exponents to solve problems
merely moving the expression which contains the exponent to the other position in the fraction

17. Notice that the sign of an exponent may be changed by
zero power
merely moving the expression which contains the exponent to the other position in the fraction
A root
the power is positive

18. Mark off as many decimal places in the product as there are
Raising to a power
Decimal places in the factors together
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
The operation of raising a number to a power

19. Depending on whether the exponent of the base is odd or even.
The process of finding a root
negative exponents arise
INDEX of the root
The number of minus signs is odd or even -

20. The law of exponents for multiplication may be stated as follows:
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 occurs as an exponent
Decimal places in the factors together

21. 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 power is negative
Imaginary 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.

22. The square of a real number is
its value is 1
The 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.
Positive

23. The indicated square root of a negative number is called an
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 number of times that the number is to be taken as a factor
Exponent
Imaginary Number

24. The power of a product is equal to the product obtained when
what power is intended and what root is intended
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
When the radical symbol is used
Raising to a power

25. 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.
Imaginary Number
The law of exponents for division
The inverse of raising a number to a power.
The number itself

26. The line above the number whose root is to be found is a symbol of grouping called the
vinculum
Is equal to the number of places in the decimal multiplied by the 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

27. 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.
The number itself
the power is negative
The number of minus signs is odd or even -

28. Any number (other than zero) raised to the _____ equals 1
The inverse of raising a number to a power.
The number itself
The law of exponents for division
zero power

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
Exponent
When the radical symbol is used
Does not Exist
merely moving the expression which contains the exponent to the other position in the fraction

30. Finding a root of a number is
keep the fraction in that form rather than express it as a mixed number
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 inverse of raising a number to a power.

31. Is a special case of multiplication in which the factors are all equal.
The operation of raising a number to a power
The law of exponents for division may be developed from this example
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
The power

32. A fractional exponent of the form 1/r indicates
a root - the index of which is r.
Exponent
its value is 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.

33. 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
Positive
number of minus signs

34. When an exponent occurs - it must always be written unless...
The laws of exponents
its value is 1
Zero occurs as an exponent
The operation of raising a number to a power

35. The laws of exponents for the power of a power may be stated as follows:
When the radical symbol is used
1
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.

36. When the exponent of a negative number is odd -
INDEX of the root
the power is negative
a root - the index of which is r.
The process of taking a root of a number

37. 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.
1
The law of exponents for division may be developed from this example
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.
Zero occurs as an exponent

38. Any number divided by itself is
the rule for fractional exponents to solve problems
The process of finding a root
1
The number of minus signs is odd or even -

39. Any number divided by itself results in a _________ and has a value of 1
Is equal to the number of places in the decimal multiplied by the exponent.
The law of exponents for division
0 exponent
keep the fraction in that form rather than express it as a mixed number

40. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
Decimal places in the factors together
negative exponents arise
When the radical symbol is used
keep the fraction in that form rather than express it as a mixed number

41. 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.
A root of a number
The process of taking a root of a number
Positive
Raising to a power

42. To determine the number of decimal places in the root of a perfect power
Positive
negative exponents arise
Divide the number of decimal places in the radicand by the index of the root.
When the radical symbol is used

43. 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
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
0 exponent

44. We recall that the exponent of a number tells
Raising to a power
vinculum
The number of times that the number is to be taken as a factor
zero power

45. A fraction is raised to a power by
Raising the numerator and the denominator separately to the power indicated
The law of exponents for division
One desired
zero power

46. To multiply two or more powers having the same base -
zero power
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 rule for fractional exponents to solve problems

47. In the answer to a problem such as 4^3 + 4^3.
negative exponents arise
Imaginary Number
Divide the number of decimal places in the radicand by the index of the root.
Zero occurs as an exponent

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

49. When a radical has no index - the square root is understood to be the
Real Numbers
One desired
Add the exponents and raise the common base to the sum of the exponents
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.