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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. 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 laws of exponents
Exponent
Does not Exist
Zero occurs as an exponent

2. It is important to realize that the base must be the same for each factor - in order to apply
Positive
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
The laws of exponents

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

4. Finding a root of a number is
The inverse of raising a number to a power.
Add the exponents and raise the common base to the sum of the exponents
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

5. The law of exponents for multiplication may be stated as follows:
Exponent
Add the exponents and raise the common base to the sum of the exponents
Positive
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

6. The law of exponents for multiplication may be combined with
the rule for fractional exponents to solve problems
merely moving the expression which contains the exponent to the other position in the fraction
the power is positive
The number itself

7. When an exponent occurs - it must always be written unless...
its value is 1
The process of finding a root
Raising the numerator and the denominator separately to the power indicated
Raising to a power

8. The square of a real number is
its value is 1
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
the power is negative

9. 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
what power is intended and what root is intended
The number of minus signs is odd or even -
A root

10. When the exponent is even
Raising to a power
Divide the number of decimal places in the radicand by the index of the root.
the power is positive
Exponent

11. 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.
Exponent
The inverse of raising a number to a power.
The number of times that the number is to be taken as a factor
The law of exponents for division

12. To multiply two or more powers having the same base -
Zero occurs as an exponent
the rule for fractional exponents to solve problems
a root - the index of which is r.
Add the exponents and raise the common base to the sum of the exponents

13. Notice that the sign of an exponent may be changed by
merely moving the expression which contains the exponent to the other position in the fraction
A root of a number
keep the fraction in that form rather than express it as a mixed number
The power

14. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
0 exponent
The number of minus signs is odd or even -
When the radical symbol is used
The inverse of raising a number to a power.

15. A fraction is raised to a power by
keep the fraction in that form rather than express it as a mixed number
Zero occurs as an exponent
Raising the numerator and the denominator separately to the power indicated
The laws of exponents

16. Is multiplication in which all the numbers being multiplied together are equal.
Raising to a power
Positive
The laws of exponents
merely moving the expression which contains the exponent to the other position in the fraction

17. 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
Divide the number of decimal places in the radicand by the index of the root.
negative exponents arise
The power

18. Is the inverse of raising a number to a power.
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.
the power is positive
a root - the index of which is r.

19. Is a special case of multiplication in which the factors are all equal.
INDEX of the root
The operation of raising a number to a power
the rule for fractional exponents to solve problems
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.

20. In fraction form an exponent shows immediately
A root of a number
Add the exponents and raise the common base to the sum of the exponents
Real Numbers
what power is intended and what root is intended

21. The first power of any number is
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 operation of raising a number to a power
Does not Exist
The number itself

22. The law of exponents for a power of an indicated quotient
Raising 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.
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 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.

23. 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.
Add the exponents and raise the common base to the sum of the exponents
One desired
Decimal places in the factors together

24. 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 inverse of raising a number to a power.
The power
The law of exponents for division may be developed from this example
The operation of raising a number to a power

25. A fractional exponent of the form 1/r indicates
a root - the index of which is r.
Does not Exist
the power is positive
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.

26. The laws of exponents for the power of a power may be stated as follows:
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.
The number of times that the number is to be taken as a factor
Imaginary Number

27. Positive and negative numbers belong to the class called
Decimal places in the factors together
the rule for fractional exponents to solve problems
Real Numbers
number of minus signs

28. Any number divided by itself results in a _________ and has a value of 1
number of minus signs
0 exponent
Real Numbers
its value is 1

29. If an improper fraction occurs in an exponent it is customary to
The power
The operation of raising a number 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.
keep the fraction in that form rather than express it as a mixed number

30. 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.
INDEX of the root
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
A root of a number
The process of finding a root

31. When a decimal is raised to a power - the number of decimal places in the result
Add the exponents and raise the common base to the sum of the exponents
A root
Does not Exist
Is equal to the number of places in the decimal multiplied by the exponent.

32. Any number divided by itself is
Add the exponents and raise the common base to the sum of the exponents
The power
Positive
1

33. Depending on whether the exponent of the base is odd or even.
number of minus signs
The number of minus signs is odd or even -
what power is intended and what root is intended
Is equal to the number of places in the decimal multiplied by the exponent.

34. To divide one power into another having the same base
The process of finding a 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.
One desired
its value is 1

35. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
Divide the number of decimal places in the radicand by the index of the root.
vinculum
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.

36. In the answer to a problem such as 4^3 + 4^3.
zero power
merely moving the expression which contains the exponent to the other position in the fraction
Zero occurs as an exponent
The law of exponents for division

37. 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.
Real Numbers
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.
Is equal to the number of places in the decimal multiplied by the exponent.
Exponent

38. 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.
Real Numbers
0 exponent
Raising the numerator and the denominator separately to the power indicated
The process of taking a root of a number

39. The sign of the product is determined - as in ordinary multiplication - by the
Real Numbers
number of minus signs
The process of taking a root of a number
The power

40. The line above the number whose root is to be found is a symbol of grouping called the
vinculum
keep the fraction in that form rather than express it as a mixed number
The number itself
Real Numbers

41. The law of exponents for the power of a product is as follows:
One desired
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.
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.

42. Mark off as many decimal places in the product as there are
its value is 1
Is equal to the number of places in the decimal multiplied by the 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.
Decimal places in the factors together

43. When the exponent of a negative number is odd -
The law of exponents for division may be developed from this example
number of minus signs
The inverse of raising a number to a power.
the power is negative

44. The indicated square root of a negative number is called an
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
A root of a number
Imaginary Number
The number of minus signs is odd or even -

45. The number that indicates the root is called the
INDEX of the root
a root - the index of which is r.
Raising the numerator and the denominator separately to the power indicated
The operation of raising a number to a power

46. Is the number of times the number itself is to be taken as a factor.
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.
The power
the power is positive

47. Is a special factor 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.
A root
Raising the numerator and the denominator separately to the power indicated
The laws of exponents

48. We recall that the exponent of a number tells
The inverse of raising a number to a power.
The power
The number of times that the number is to be taken as a factor
Decimal places in the factors together

49. Any number (other than zero) raised to the _____ equals 1
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.
One desired
When the radical symbol is used
zero power