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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.
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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. To divide powers of 10:
Step 1. Divide the coefficients of the terms
decrease the power-of-10 exponent by the same number of units
squared
cube-root key

2. 10 - or 1 with the decimal point moved one place to the right
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
perfect square
10^1

3. Always 10 for scientific notation
you have to adjust the value of the exponent in order avoid changing the actual value.
base
adjust the value of the coefficient
Not

4. To add powers of ten:
10^1
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0

5. Numbers with exponents can be directly multiplied or divided only when they have the
you have to adjust the value of the exponent in order avoid changing the actual value.
When the exponent of a power-of-10 expression is a negative integer:
square root
Same base

6. There are no special rules for adding and subtracting numbers that are written with exponents.
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
must be multiples of 3 or 0
Because 4 multiplied by itself equals 16.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

7. To multiply or divide exponent terms that do not have the same base:
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
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
0

8. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
9 (3^2 = 9)
10^-18
2 x 10^9
1. Multiply the coefficients 2. Add the exponents

9. Any number with an exponent of 1 is equal to
exponent
itself
perfect square
move the decimal point the same number of units to the left

10. To add or subtract numbers written with exponents:
the radical sign with a little 3 that indicates the cube root:
a fractional decimal
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

11. Dividing by 10
Moving the decimal point to the left
1
change both terms in order to keep the value the same.
one digit to the left of the decimal point

12. Scientific notation requires there to be only
one digit to the left of the decimal point
0
2
base

13. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
Moving the decimal point to the right
same exponent
2

14. 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
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
one digit to the left of the decimal point
the radical sign with a little 3 that indicates the cube root:

15. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
1. Multiply the coefficients 2. Add the exponents
When moving the decimal point to the left (dividing by 10)
1. Divide the coefficients 2. Subtract the exponents

16. Valid powers of 10 for engineering notation are:
1. Multiply the coefficients 2. Add the exponents
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
6.74 x 10^-7
squared

17. The cube root of zero is
0
Subtract the exponent
change both terms in order to keep the value the same.
cube-root key

18. Multiplying by 10
1
Moving the decimal point to the right
Scientific notation
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

19. Any number with an exponent of 0 is equal to
Not
Are Equal
cube-root key
1

20. Increase the value of the exponent by 1 (multiplying by 10)
rewrite one of the terms so that the exponents are equal
When moving the decimal point to the left (dividing by 10)
perfect square
Same base

21. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
10^2
0
negative number

22. 3^0 =
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
The solution exists - but not in the real number system.
decrease the power-of-10 exponent by the same number of units
1

23. To divide powers that have the same base:
Moving the decimal point to the left
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
0
1

24. 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
1
cube-root key
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
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

25. To find the square root of any number - simply key in the number (the radicand) and press the
Not
exponent
Calculator square-root key
Moving the decimal point to the right

26. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
coefficient
you have to adjust the value of the exponent in order avoid changing the actual value.
Not

27. 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.
square root
The solution exists - but not in the real number system.
perfect square
exponent

28. Any number with a negative exponent is equal to
negative number
Because 4 multiplied by itself equals 16.
exponent
1 divided by that number with a positive exponent

29. = 0.1 - or 1 with the decimal point moved one place to the left.
Calculator square-root key
coefficient
To multiply powers that have the same base:
10^-1

30. 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.
Engineering notation
2
increase the power-of-10 exponent by the same number of units
radical sign

31. When you decrease the value of the power-of-10 exponent
proper scientific
exponent
move the decimal point the same number of units to the right
5

32. 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
1
change both terms in order to keep the value the same.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left

33. 0^5 =
0
adjust the value of the coefficient
proper scientific
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.

34. 100 - or 1 with the decimal point moved two places to the right
cube-root key
0
5
10^2

35.
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
rewrite one of the terms so that the exponents are equal
you have to adjust the value of the exponent in order avoid changing the actual value.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

36. 1 to any power is equal to
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
base
1
decrease the value of the exponent by 1 (dividing by 10)

37. Negative cube roots are okay ... negative square roots are
negative number
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Not
10^-2

38. When moving the decimal point to the right (multiplying by 10)
rewrite one of the terms so that the exponents are equal
Because 4 multiplied by itself equals 16.
decrease the value of the exponent by 1 (dividing by 10)
Not

39. A number with an exponent of 3 is often said to be
cubed
a fractional decimal
same exponent
cube-root key

40. For the 10
move the decimal point the same number of units to the right
Step 1. Divide the coefficients of the terms
5
exponent

41. 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
5
adjust the value of the coefficient
Moving the decimal point to the left
Scientific notation

42. 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
squared
coefficient
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
1. Divide the coefficients 2. Subtract the exponents

43. A number - when multiplied by itself - is equal to a given number.
same exponent
square root
3
Not

44. 5^1 =
exponent
10^1
6.74 x 10^-7
5

45. To subtract powers of ten:
0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
adjust the value of the coefficient
1

46. The square of 3 is
3
To multiply powers that have the same base:
cubed
9 (3^2 = 9)

47. Step 1: Add the exponents Step 2: Use the common base
negative number
To multiply powers that have the same base:
1
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.

48. Indicates the number of times the base is to be multiplied.
Step 1. Divide the coefficients of the terms
exponent
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

49. = 0.01 - or 1 with the decimal point moved two places to the left.
adjust the value of the coefficient
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
2
10^-2

50. A number is a second number which - when multiplied by itself three times - equals the original number.
When moving the decimal point to the left (dividing by 10)
squared
cube root
decrease the value of the exponent by 1 (dividing by 10)