Test your basic knowledge |

CLEP General Mathematics: Exponents And Radicals

Subjects : clep, math

Instructions:

Answer 49 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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 first power of any number is
the power is negative
The number itself
The number of times that the number is to be taken as a factor
Is equal to the number of places in the decimal multiplied by the exponent.

2. The laws of exponents for the power of a power may be stated as follows:
The laws of exponents
INDEX of the root
Real Numbers
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.

3. 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 operation of raising a number to a power
a root - the index of which is r.
Does not Exist
Zero occurs as an exponent

4. If the law of exponents for division is extended to include cases where the exponent of the denominator is larger
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.
negative exponents arise
1

5. The power of a product is equal to the product obtained when
merely moving the expression which contains the exponent to the other position in the fraction
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
The process of taking a root of a number
The number of times that the number is to be taken as a factor

6. Is multiplication in which all the numbers being multiplied together are equal.
number of minus signs
The laws of exponents
what power is intended and what root is intended
Raising to a power

7. 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 rule for fractional exponents to solve problems
The law of exponents for division may be developed from this example
The inverse of raising a number to a power.
When the radical symbol is used

8. 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.
One desired
The number of minus signs is odd or even -
The law of exponents for division

9. We recall that the exponent of a number tells
0 exponent
Real Numbers
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

10. It is important to realize that the base must be the same for each factor - in order to apply
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 laws of exponents
Decimal places in the factors together
The number itself

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

12. 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.
zero power
the power is negative
The inverse of raising a number to a power.

13. The sign of the product is determined - as in ordinary multiplication - by the
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
Add the exponents and raise the common base to the sum of the exponents
number of minus signs
Positive

14. 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
1
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.

15. 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 operation of raising a number to a power
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.
vinculum
A root of a number

16. The indicated square root of a negative number is called an
Does not Exist
Imaginary Number
When the radical symbol is used
The process of finding a root

17. The number that indicates the root is called the
INDEX of the root
0 exponent
Does not Exist
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.

18. Is the number of times the number itself is to be taken as a factor.
The law of exponents for division
The 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.
Add the exponents and raise the common base to the sum of the exponents

19. A fraction is raised to a power by
INDEX of the root
Divide the number of decimal places in the radicand by the index of the root.
The inverse of raising a number to a power.
Raising the numerator and the denominator separately to the power indicated

20. Is the inverse of raising a number to a power.
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
Real Numbers
The process of finding a root

21. Mark off as many decimal places in the product as there are
INDEX of the root
negative exponents arise
0 exponent
Decimal places in the factors together

22. When an exponent occurs - it must always be written unless...
its value is 1
Exponent
Raising the numerator and the denominator separately to the power indicated
Divide the number of decimal places in the radicand by the index of the root.

23. The law of exponents for multiplication may be stated as follows:
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
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.
zero power

24. To determine the number of decimal places in the root of a perfect power
what power is intended and what root is intended
The process of finding a root
Divide the number of decimal places in the radicand by the index of the root.
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together

25. Any number divided by itself results in a _________ and has a value of 1
0 exponent
zero power
The law of exponents for division may be developed from this example
The process of finding a root

26. When a decimal is raised to a power - the number of decimal places in the result
its value is 1
Is equal to the number of places in the decimal multiplied by the exponent.
The power
negative exponents arise

27. Positive and negative numbers belong to the class called
A root
Real Numbers
the power is positive
The operation of raising a number to a power

28. In fraction form an exponent shows immediately
The number itself
what power is intended and what root is intended
Raising the numerator and the denominator separately to the power indicated
Is equal to the number of places in the decimal multiplied by the exponent.

29. When the exponent is even
INDEX of the root
Zero occurs as an exponent
the power is 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.

30. Finding a root of a number is
The inverse of raising a number to a power.
Positive
The operation of raising a number to a power
INDEX of the root

31. If an improper fraction occurs in an exponent it is customary to
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.
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

32. When a radical has no index - the square root is understood to be the
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.
the power is negative
Does not Exist

33. In the answer to a problem such as 4^3 + 4^3.
Does not Exist
Zero occurs as an exponent
The law of exponents for division may be developed from this example
Raising the numerator and the denominator separately to the power indicated

34. We conclude that a number N with a negative exponent is equivalent to a fraction having the following form:
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.
Imaginary Number
The process of taking a root of a number

35. A fractional exponent of the form 1/r indicates
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.
merely moving the expression which contains the exponent to the other position in the fraction
a root - the index of which is r.

36. The square of a real number is
The operation of raising a number to a power
Positive
The number of minus signs is odd or even -
The process of finding a root

37. To multiply two or more powers having the same base -
Does not Exist
Add the exponents and raise the common base to the sum of the exponents
Positive
1

38. 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.
its value is 1
merely moving the expression which contains the exponent to the other position in the fraction
Exponent
zero power

39. Is a special factor of a number.
A root
a root - the index of which is r.
its value is 1
Does not Exist

40. Depending on whether the exponent of the base is odd or even.
The number of minus signs is odd or even -
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
what power is intended and what root is intended
Zero occurs as an exponent

41. To divide one power into another having the same base
zero power
vinculum
Decimal places in the factors together
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. The law of exponents for multiplication may be combined with
the rule for fractional exponents to solve problems
zero power
The laws of exponents
Divide the number of decimal places in the radicand by the index of the root.

43. The law of exponents for the power of a product is as follows:
The number of minus signs is odd or even -
1
The 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.

44. 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.
Is equal to the number of places in the decimal multiplied by the exponent.
When the radical symbol is used
The process of taking a root 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.

45. Any number divided by itself is
Each of the original factors is raised to the indicated power and the resulting powers are multiplied together
1
The law of exponents for division may be developed from this example
0 exponent

46. Notice that the sign of an exponent may be changed by
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.
Real Numbers
merely moving the expression which contains the exponent to the other position in the fraction
A root of a number

47. When the exponent of a negative number is odd -
Divide the number of decimal places in the radicand by the index of the root.
the power is negative
The number itself
When the radical symbol is used

48. Is a special case of multiplication in which the factors are all equal.
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 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.
Real Numbers
The operation of raising a number to a power

49. The line above the number whose root is to be found is a symbol of grouping called the
merely moving the expression which contains the exponent to the other position in the fraction
vinculum
To multiply two or more powers having the same base - add the exponents and raise the common base to the sum of the exponents.
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.