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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. Positive and negative numbers belong to the class called
Real Numbers
its value is 1
1
Add the exponents and raise the common base to the sum of the exponents

2. The sign of the product is determined - as in ordinary multiplication - by the
Real Numbers
The process of finding a root
number of minus signs
A root of a number

3. To multiply two or more powers having the same base -
Add the exponents and raise the common base to the sum of the exponents
0 exponent
When the radical symbol is used
Zero occurs as an exponent

4. In the answer to a problem such as 4^3 + 4^3.
Zero occurs as an exponent
Imaginary Number
vinculum
The process of finding a root

5. Is the inverse of raising a number to a power.
Real Numbers
1
The process of finding a root
keep the fraction in that form rather than express it as a mixed number

6. Is a special factor of a number.
A root of a number
its value is 1
what power is intended and what root is intended
A root

7. Finding a root of a number is
The operation of raising a number to a power
The inverse of raising a number to a power.
the power is negative
The number of minus signs is odd or even -

8. The law of exponents for multiplication may be combined with
The process of taking a root of a number
INDEX of the root
the rule for fractional exponents to solve problems
merely moving the expression which contains the exponent to the other position in the fraction

9. 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.
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
Imaginary Number
Exponent

10. We recall that the exponent of a number tells
One desired
The number of times that the number is to be taken as a factor
vinculum
Does not Exist

11. Any number divided by itself is
Imaginary Number
1
the rule for fractional exponents to solve problems
Add the exponents and raise the common base to the sum of the exponents

12. Depending on whether the exponent of the base is odd or even.
The process of finding a root
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
The number of minus signs is odd or even -

13. When a radical has no index - the square root is understood to be the
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.
One desired
The number of times that the number is to be taken as a factor

14. When the exponent of a negative number is odd -
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 finding a root
0 exponent
the power is negative

15. The number that indicates the root is called the
INDEX of the root
The process of taking a root of a number
The law of exponents for division may be developed from this example
Is equal to the number of places in the decimal multiplied by the exponent.

16. Is a special case of multiplication in which the factors are all equal.
The operation 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.
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.

17. To divide one power into another having the same base
merely moving the expression which contains the exponent to the other position in the fraction
Zero occurs as an exponent
INDEX of the root
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.

18. Any number (other than zero) raised to the _____ equals 1
Zero occurs as an 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.
INDEX of the root
zero power

19. In fraction form an exponent shows immediately
INDEX of the root
what power is intended and what root is intended
the power is positive
keep the fraction in that form rather than express it as a mixed number

20. To determine the number of decimal places in the root of a perfect power
The process of taking a root of a number
A root of a number
The power
Divide the number of decimal places in the radicand by the index of the root.

21. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
The number of minus signs is odd or even -
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.
the power is negative

22. 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 operation of raising a number to a power
Imaginary Number
Raising the numerator and the denominator separately to the power indicated
The process of taking a root of a number

23. When an exponent occurs - it must always be written unless...
its value is 1
keep the fraction in that form rather than express it as a mixed number
Does not Exist
Raising to a power

24. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
Add the exponents and raise the common base to the sum of the exponents
negative exponents arise
The operation of raising a number to a power
vinculum

25. The laws of exponents for the power of a power may be stated 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
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.
Is equal to the number of places in the decimal multiplied by the exponent.

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

27. Since there is no real number whose square is a negative number - it is sometimes said that the square root of a negative number
A root of a number
vinculum
Does not Exist
the power is negative

28. If an improper fraction occurs in an exponent it is customary to
Divide the number of decimal places in the radicand by the index of the root.
a root - the index of which is r.
The law of exponents for division
keep the fraction in that form rather than express it as a mixed number

29. Notice that the sign of an exponent may be changed by
its value is 1
The number itself
A root
merely moving the expression which contains the exponent to the other position in the fraction

30. 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.
a root - the index of which is r.
Imaginary Number
vinculum

31. The law of exponents for the power of a product is as follows:
the rule for fractional exponents to solve problems
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.
Is equal to the number of places in the decimal multiplied by the exponent.
Real Numbers

32. Mark off as many decimal places in the product as there are
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
The number of minus signs is odd or even -
Decimal places in the factors together

33. The square of a real number is
0 exponent
Positive
the power is positive
The power

34. The power of a product is equal to the product obtained when
The power
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Positive
Raising to a power

35. 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.
Raising the numerator and the denominator separately to the power indicated
The process of taking a root of a number
The law of exponents for division
The number of times that the number is to be taken as a factor

36. 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.
The inverse of raising a number to a power.
the power is positive
A root of a number
The laws of exponents

37. When the exponent is even
the power is positive
a root - the index of which is r.
negative exponents arise
0 exponent

38. The indicated square root of a negative number is called an
A root of a number
The process of finding a root
Positive
Imaginary Number

39. Is the number of times the number itself is to be taken as a factor.
The power
The inverse of raising a number to a power.
what power is intended and what root is intended
Zero occurs as an exponent

40. 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 operation 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.
negative exponents arise

41. It is important to realize that the base must be the same for each factor - in order to apply
1
The laws of exponents
The law of exponents for division
The inverse of raising a number to a power.

42. A fraction is raised to a power by
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 the numerator and the denominator separately to the power indicated
The laws of exponents
The inverse of raising a number to a power.

43. Any number divided by itself results in a _________ and has a value of 1
the power is negative
0 exponent
1
zero power

44. 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 number of minus signs is odd or even -
Positive
The law of exponents for division may be developed from this example
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.

45. The law of exponents for multiplication may be stated as follows:
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.
One desired
The law of exponents for division may be developed from this example

46. A fractional exponent of the form 1/r indicates
merely moving the expression which contains the exponent to the other position in the fraction
The power
The law of exponents for division
a root - the index of which is r.

47. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
merely moving the expression which contains the exponent to the other position in the fraction
When the radical symbol is used
Divide the number of decimal places in the radicand by the index of the root.
Exponent

48. Is multiplication in which all the numbers being multiplied together are equal.
Real Numbers
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.
Raising to a power

49. The first power of any number is
The number itself
the power is negative
The process of taking a root of a number
a root - the index of which is r.