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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. When you move the decimal point in the coefficient to the left
base
increase the power-of-10 exponent by the same number of units
negative number
0

2. To add or subtract numbers written with exponents:
1
3
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.

3. The decimal part
2
you have to adjust the value of the exponent in order avoid changing the actual value.
coefficient
proper scientific

4. Any number with a negative exponent is equal to
negative number
same exponent
1
1 divided by that number with a positive exponent

5. A number with an exponent of 2 is often said to be
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
adjust the value of the coefficient
squared
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

6. To divide powers of ten:
the radical sign with a little 3 that indicates the cube root:
base
1. Divide the coefficients 2. Subtract the exponents
Subtract the exponent

7. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
exponent
1
0

8. 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)
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0

9. Any number with an exponent of 0 is equal to
The solution exists - but not in the real number system.
1
0
move the decimal point the same number of units to the right

10. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
6.74 x 10^-7
0
same exponent

11. The cube root of zero is
Not
0
coefficient
3

12. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
10^2
negative number
Subtract the exponent
1

13. When you change the position of the decimal point in a coefficient value
2
you have to adjust the value of the exponent in order avoid changing the actual value.
Because 4 multiplied by itself equals 16.
When the exponent of a power-of-10 expression is a negative integer:

14. Indicates the number of times the base is to be multiplied.
1
coefficient
exponent
0

15. 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.
change both terms in order to keep the value the same.
When moving the decimal point to the left (dividing by 10)
Engineering notation
To multiply powers that have the same base:

16. 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
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
square root
Moving the decimal point to the left
change both terms in order to keep the value the same.

17. Multiplying by 10
Moving the decimal point to the right
1
you have to adjust the value of the exponent in order avoid changing the actual value.
10^1

18. 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
To multiply powers that have the same base:
5
0

19. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
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.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1

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

21. Valid powers-of-10 for engineering notation
decrease the power-of-10 exponent by the same number of units
must be multiples of 3 or 0
coefficient
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

22. 0^5 =
cubed
0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
negative number

23. A number - when multiplied by itself - is equal to a given number.
cube-root key
square root
10^-18
To multiply powers that have the same base:

24. 3^0 =
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
9 (3^2 = 9)
move the decimal point the same number of units to the right
1

25. The symbol for the cube root of a number is
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
itself
the radical sign with a little 3 that indicates the cube root:
3

26. 100 - or 1 with the decimal point moved two places to the right
10^-1
10^2
cubed
Are Equal

27. For the 10
exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
9 (3^2 = 9)
move the decimal point the same number of units to the left

28. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
must be multiples of 3 or 0
rewrite one of the terms so that the exponents are equal
Are Equal

29. When you move the decimal point in the coefficient to the right
1
decrease the power-of-10 exponent by the same number of units
proper scientific
perfect square

30. To add powers of ten:
itself
one digit to the left of the decimal point
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

31. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1. Multiply the coefficients 2. Add the exponents
must be multiples of 3 or 0
10^2
2

32. Don't bother trying to find the square root of a negative number.
The solution exists - but not in the real number system.
When moving the decimal point to the left (dividing by 10)
exponent
Moving the decimal point to the right

33. Valid powers of 10 for engineering notation are:
0
10^2
Because 4 multiplied by itself equals 16.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

34. 5^1 =
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
5
decrease the value of the exponent by 1 (dividing by 10)
Same base

35. 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
Not
The solution exists - but not in the real number system.
10^-2
cube-root key

36. Adding and subtracting powers of ten can be a bit more complicated than multiplying and dividing. The main problem is that powers of ten can be added or subtracted only when both terms have the
1
coefficient
itself
same exponent

37. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
10^2
Scientific notation
2 x 10^9
3

38. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
move the decimal point the same number of units to the left
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
decrease the value of the exponent by 1 (dividing by 10)

39. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
2
Same base
move the decimal point the same number of units to the left

40. 1^4 =
Moving the decimal point to the left
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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

41. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
The solution exists - but not in the real number system.
cubed
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

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

43. To divide powers of 10:
When the exponent of a power-of-10 expression is a negative integer:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Divide the coefficients of the terms
one digit to the left of the decimal point

44. To multiply or divide exponent terms that do not have the same base:
base
you have to adjust the value of the exponent in order avoid changing the actual value.
5
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

45. The square root of 9 is
Scientific notation
3
2
base

46. The square of 3 is
increase the power-of-10 exponent by the same number of units
9 (3^2 = 9)
0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

47. 1 to any power is equal to
decrease the power-of-10 exponent by the same number of units
you have to adjust the value of the exponent in order avoid changing the actual value.
1
same exponent

48. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
10^1
10^2
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

49. 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.
negative number
Scientific notation
1
cubed

50. = 0.01 - or 1 with the decimal point moved two places to the left.
2 x 10^9
10^2
3
10^-2