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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. When an exponent occurs - it must always be written unless...
The laws of exponents
The law of exponents for division
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 value is 1

2. Is the inverse of raising a number to a power.
vinculum
The operation of raising a number to a power
One desired
The process of finding a root

3. 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.
1
The law of exponents for division
A root of a number
The inverse of raising a number to a power.

4. 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 power
a root - the index of which is r.
Raising to a power

5. 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.
a root - the index of which is r.
Raising to a power
One desired

6. A fraction is raised to a power by
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.
negative exponents arise
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

7. Depending on whether the exponent of the base is odd or even.
merely moving the expression which contains the exponent to the other position in the fraction
Divide the number of decimal places in the radicand by the 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.
The number of minus signs is odd or even -

8. When the exponent of a negative number is odd -
Divide the number of decimal places in the radicand by the index of the root.
negative exponents arise
the power is negative
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.

9. The law of exponents for a power of an indicated quotient
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 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.
merely moving the expression which contains the exponent to the other position in the fraction
When the radical symbol is used

10. Any number divided by itself is
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
1
merely moving the expression which contains the exponent to the other position in the fraction
its value is 1

11. The law of exponents for multiplication may be stated as follows:
what power is intended and what root is intended
Zero occurs as an exponent
Is equal to the number of places in the decimal multiplied by the exponent.
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

12. 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
number of minus signs
Imaginary Number

13. 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 rule for fractional exponents to solve problems
The power
Decimal places in the factors together

14. A fractional exponent of the form 1/r indicates
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 power
a root - the index of which is r.
the rule for fractional exponents to solve problems

15. When the exponent is even
One desired
what power is intended and what root is intended
the power is positive
The number of minus signs is odd or even -

16. 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
A root of a number
the power is negative
When the radical symbol is used

17. The power of a product is equal to the product obtained when
the power is negative
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Raising the numerator and the denominator separately to the power indicated
0 exponent

18. The indicated square root of a negative number is called an
Add the exponents and raise the common base to the sum of the exponents
Decimal places in the factors together
Imaginary Number
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.

19. 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.
A root
When the radical symbol is used
keep the fraction in that form rather than express it as a mixed number

20. 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 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.
0 exponent
The number of times that the number is to be taken as a factor
The law of exponents for division

21. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
negative exponents arise
The laws of exponents
One desired
INDEX of the root

22. Any number (other than zero) raised to the _____ equals 1
The power
Is equal to the number of places in the decimal multiplied by the exponent.
The number itself
zero power

23. The sign of the product is determined - as in ordinary multiplication - by the
keep the fraction in that form rather than express it as a mixed number
1
number of minus signs
negative exponents arise

24. Is a special case of multiplication in which the factors are all equal.
keep the fraction in that form rather than express it as a mixed number
The operation of raising a number to a power
merely moving the expression which contains the exponent to the other position in the fraction
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.

25. When a decimal is raised to a power - the number of decimal places in the result
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
The number itself
Is equal to the number of places in the decimal multiplied by the exponent.
negative exponents arise

26. The law of exponents for the power of a product is as follows:
zero power
The law of exponents for division
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 rule for fractional exponents to solve problems

27. 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.
keep the fraction in that form rather than express it as a mixed number
Real Numbers
The law of exponents for division may be developed from this example
Zero occurs as an exponent

28. The law of exponents for multiplication may be combined with
The laws of 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.
0 exponent

29. The number that indicates the root is called the
Zero occurs as an exponent
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
INDEX of the root

30. Any number divided by itself results in a _________ and has a value of 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.
0 exponent
The number itself
The laws of exponents

31. The line above the number whose root is to be found is a symbol of grouping called the
Zero occurs as an exponent
The number of minus signs is odd or even -
vinculum
zero power

32. To determine the number of decimal places in the root of a perfect power
The number of minus signs is odd or even -
One desired
The power
Divide the number of decimal places in the radicand by the index of the root.

33. When a radical has no index - the square root is understood to be the
One desired
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.
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 negative

34. 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.
zero power
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.

35. Finding a root of a number is
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 inverse of raising a number to a power.
The process of finding a root
number of minus signs

36. In the answer to a problem such as 4^3 + 4^3.
Raising the numerator and the denominator separately to the power indicated
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 laws of exponents
Zero occurs as an exponent

37. The laws of exponents for the power of a power may be stated as follows:
The number itself
a root - the index of which is r.
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.
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.

38. It is important to realize that the base must be the same for each factor - in order to apply
The operation 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
Does not Exist
The laws of exponents

39. 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.
Exponent
The process of taking a root of a number
One desired
its value is 1

40. Is the number of times the number itself is to be taken as a factor.
The power
Decimal places in the factors together
A root
A root of a number

41. 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
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.

42. 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 power is negative
a root - the index of which is r.
Does not Exist
The power

43. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
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.
The process of finding a root
1

44. 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.
a root - the index of which is r.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
The law of exponents for division may be developed from this example
Exponent

45. In fraction form an exponent shows immediately
what power is intended and what root is intended
Is equal to the number of places in the decimal multiplied by the exponent.
The number of minus signs is odd or even -
number of minus signs

46. The square of a real number is
Positive
The number of minus signs is odd or even -
Raising to a power
A root of a number

47. Positive and negative numbers belong to the class called
Is equal to the number of places in the decimal multiplied by the exponent.
Real Numbers
The law of exponents for division may be developed from this example
One desired

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

49. A vinculum - long enough to extend over the entire expression whose root is to be found - should be attached.
Real Numbers
When the radical symbol is used
The number itself
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.