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CLEP General Mathematics: Powers Exponents And Roots

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
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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. To find the cube root of any number - simply key in the number (the radicand) and press cube-root key. On most calculators - the cube-root function is a 2nd level function. This means you have to press the 2nd key before pressing the key for the
2 x 10^9
cube-root key
decrease the value of the exponent by 1 (dividing by 10)
the radical sign with a little 3 that indicates the cube root:

2. When you increase the value of the power-of-10 exponent
Calculator square-root key
radical sign
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
move the decimal point the same number of units to the left

3. The square root of 9 is
Because 4 multiplied by itself equals 16.
Scientific notation
3
the radical sign with a little 3 that indicates the cube root:

4. To divide powers of 10:
10^-1
Step 1. Divide the coefficients of the terms
move the decimal point the same number of units to the right
exponent

5. When moving the decimal point to the right (multiplying by 10)
base
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
decrease the value of the exponent by 1 (dividing by 10)

6. A number is a second number which - when multiplied by itself three times - equals the original number.
base
cube root
0
2

7. Dividing by 10
Moving the decimal point to the left
2 x 10^9
The solution exists - but not in the real number system.
5

8. Is a special form of power-of-10 notation where the exponents for the 10s must be 0 or multiples of 3. There must be 1 - 2 - or 3 digits on the left side of the decimal point.
cube root
perfect square
When the exponent of a power-of-10 expression is a negative integer:
Engineering notation

9. For the 10
1
exponent
increase the power-of-10 exponent by the same number of units
Step 1. Multiply the coefficients of the factors. The result is the coefficient of the product. Step 2. Add the exponents of the factors. The result is the exponent of the product. Of course the base of 10 remains unchanged.

10. Indicates the number to be multiplied.
proper scientific
10^1
base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

11. Because the exponent for the base-10 must be 0 or a multiple of 3 - the coefficient cannot always be a value between -9 and 9. Instead - the coefficients for engineering notation will be between
Because the exponent for the base-10 must be 0 or a multiple of 3 - the coefficient cannot always be a value between -9 and 9. Instead - the coefficients for engineering notation will be between
Calculator square-root key
10^1
10^-1

12. 3^0 =
coefficient
Same base
one digit to the left of the decimal point
1

13. Scientific notation requires there to be only
one digit to the left of the decimal point
adjust the value of the coefficient
Determine the number of times the original decimal has to be multiplied or divided by 10 in order to show one non-zero digit to the left of the decimal point. Multiply the normalized value by a power of 10 that will restore equality. If you multiplie
Step 1. Divide the coefficients of the terms

14.
square root
1
move the decimal point the same number of units to the left
Determine the number of times the original decimal has to be multiplied or divided by 10 in order to show one non-zero digit to the left of the decimal point. Multiply the normalized value by a power of 10 that will restore equality. If you multiplie

15. Negative cube roots are okay ... negative square roots are
1
1 divided by that number with a positive exponent
Not
The solution exists - but not in the real number system.

16. Any number with an exponent of 0 is equal to
When the exponent of a power-of-10 expression is a negative integer:
itself
Scientific notation
1

17. When you change the position of the decimal point in a coefficient value
you have to adjust the value of the exponent in order avoid changing the actual value.
base
0
9 (3^2 = 9)

18. When working with scientific notation - you are often required to change the location of the decimal point in the coefficient - but when you move the decimal point - you must
To multiply powers that have the same base:
1
change both terms in order to keep the value the same.
adjust the value of the coefficient

19. The square of 3 is
cube root
Not
same exponent
9 (3^2 = 9)

20. A number - when multiplied by itself - is equal to a given number.
square root
move the decimal point the same number of units to the right
0
9 (3^2 = 9)

21. A number with an exponent of 3 is often said to be
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
adjust the value of the coefficient
Calculator square-root key
cubed

22. To divide powers of ten:
1. Multiply the coefficients 2. Add the exponents
must be multiples of 3 or 0
10^2
1. Divide the coefficients 2. Subtract the exponents

23. To find the square root of any number - simply key in the number (the radicand) and press the
the radical sign with a little 3 that indicates the cube root:
you have to adjust the value of the exponent in order avoid changing the actual value.
0
Calculator square-root key

24. Allows you to express very large and very small numbers without using large numbers of digits and decimal places. It's all done with powers of ten.
Scientific notation
move the decimal point the same number of units to the right
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
you have to adjust the value of the exponent in order avoid changing the actual value.

25. Represents 1 preceded by 17 zeros and a decimal point.
cube-root key
10^2
10^-18
1. Divide the coefficients 2. Subtract the exponents

26. When working with powers of ten and scientific notation it is often necessary to adjust the position of the decimal point in the coefficient or to change the value of the exponent. When changing one of these terms - it is important that
When the exponent of a power-of-10 expression is a negative integer:
proper scientific
change both terms in order to keep the value the same.
Calculator square-root key

27. Step 1: Add the exponents Step 2: Use the common base
Because 4 multiplied by itself equals 16.
To multiply powers that have the same base:
Moving the decimal point to the left
Subtract the exponent

28. Indicates the number of times the base is to be multiplied.
exponent
10^-1
Same base
square root

29. When you move the decimal point in the coefficient to the left
move the decimal point the same number of units to the right
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
increase the power-of-10 exponent by the same number of units
rewrite one of the terms so that the exponents are equal

30. The symbol for the square root of a number is the - a sign placed in front of an expression to denote that a root is to be extracted.
change both terms in order to keep the value the same.
radical sign
the radical sign with a little 3 that indicates the cube root:
cube root

31. The square root of zero is
10^1
0
10^-1
When moving the decimal point to the left (dividing by 10)

32. An integer that is found by squaring another integer. You already know how to find the square root of 25 because it is a perfect square: 5 x 5 = 25 - or you could write it as 52 = 25. So 25 is a perfect square - and its square root is 5.
1
Step 1. Divide the coefficients of the terms
perfect square
change both terms in order to keep the value the same.

33. To divide powers that have the same base:
proper scientific
change both terms in order to keep the value the same.
To multiply powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

34. The decimal part
10^-1
1. Multiply the coefficients 2. Add the exponents
When moving the decimal point to the left (dividing by 10)
coefficient

35. 100 - or 1 with the decimal point moved two places to the right
Calculator square-root key
1
10^2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

36. Numbers with exponents can be directly multiplied or divided only when they have the
a fractional decimal
Scientific notation
Same base
When moving the decimal point to the left (dividing by 10)

37. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Not
a fractional decimal
move the decimal point the same number of units to the right
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

38. A number with an exponent of 2 is often said to be
squared
1
increase the power-of-10 exponent by the same number of units
Are Equal

39. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
coefficient
squared
Subtract the exponent

40. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
change both terms in order to keep the value the same.
10^-1
same exponent

41. Powers of ten can be added or subtracted only when their exponents
0
Are Equal
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
2

42. To multiply or divide exponent terms that do not have the same base:
1. Multiply the coefficients 2. Add the exponents
5
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1

43. The symbol for the cube root of a number is
radical sign
exponent
1. Multiply the coefficients 2. Add the exponents
the radical sign with a little 3 that indicates the cube root:

44. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
10^2
proper scientific
adjust the value of the coefficient

45. 10 - or 1 with the decimal point moved one place to the right
1
2 x 10^9
10^1
Calculator square-root key

46. 0^5 =
Scientific notation
negative number
1
0

47. To add or subtract numbers written with exponents:
Determine the number of times the original decimal has to be multiplied or divided by 10 in order to show one non-zero digit to the left of the decimal point. Multiply the normalized value by a power of 10 that will restore equality. If you multiplie
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Multiply the coefficients of the factors. The result is the coefficient of the product. Step 2. Add the exponents of the factors. The result is the exponent of the product. Of course the base of 10 remains unchanged.
move the decimal point the same number of units to the right

48. What number multiplied by itself is equal to 16? The answer is 4. Why?
change both terms in order to keep the value the same.
Because 4 multiplied by itself equals 16.
Moving the decimal point to the right
0

49. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
When the exponent of a power-of-10 expression is a negative integer:
move the decimal point the same number of units to the right
1 divided by that number with a positive exponent

50. 10^-1 = 0.1 - or 1 with the decimal point moved one place to the left. 10^-2 = 0.01 - or 1 with the decimal point moved two places to the left. 10^-18 represents 1 preceded by 17 zeros and a decimal point.
1
6.74 x 10^-7
When the exponent of a power-of-10 expression is a negative integer:
you have to adjust the value of the exponent in order avoid changing the actual value.