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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 multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
1 divided by that number with a positive exponent
0
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.

2. 10 - or 1 with the decimal point moved one place to the right
10^1
rewrite one of the terms so that the exponents are equal
1
base

3. Scientific notation requires there to be only
exponent
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
squared
one digit to the left of the decimal point

4. Dividing by 10
must be multiples of 3 or 0
one digit to the left of the decimal point
The solution exists - but not in the real number system.
Moving the decimal point to the left

5. 1 to any power is equal to
1
you have to adjust the value of the exponent in order avoid changing the actual value.
increase the power-of-10 exponent by the same number of units
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

6. To divide powers of ten:
Scientific notation
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Are Equal
1. Divide the coefficients 2. Subtract the exponents

7. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
increase the power-of-10 exponent by the same number of units
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
proper scientific
1. Divide the coefficients 2. Subtract the exponents

8. Increase the value of the exponent by 1 (multiplying by 10)
exponent
When moving the decimal point to the left (dividing by 10)
10^-18
Moving the decimal point to the right

9. Valid powers-of-10 for engineering notation
decrease the power-of-10 exponent by the same number of units
cube-root key
must be multiples of 3 or 0
Because 4 multiplied by itself equals 16.

10. Valid powers of 10 for engineering notation are:
When the exponent of a power-of-10 expression is a negative integer:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

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

12. The decimal part
1
1
coefficient
2 x 10^9

13. To add or subtract numbers 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
increase the power-of-10 exponent by the same number of units
10^-18
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

14. A number - when multiplied by itself - is equal to a given number.
10^2
square root
Calculator square-root key
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

15. 100 - or 1 with the decimal point moved two places to the right
10^2
0
1
squared

16. 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. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
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
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
change both terms in order to keep the value the same.

17. When you increase the value of the power-of-10 exponent
1. Divide the coefficients 2. Subtract the exponents
move the decimal point the same number of units to the left
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

18. 0^5 =
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Calculator square-root key
0
change both terms in order to keep the value the same.

19. When moving the decimal point to the right (multiplying by 10)
must be multiples of 3 or 0
decrease the value of the exponent by 1 (dividing by 10)
proper scientific
10^-2

20. The square root of zero is
To multiply powers that have the same base:
0
10^2
base

21. 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
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
same exponent
1
Because 4 multiplied by itself equals 16.

22. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
itself
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
2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

23. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Scientific notation
a fractional decimal
radical sign
Because 4 multiplied by itself equals 16.

24. A very small number such as 0.000000674 can be written with scientific notation as
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
1. Divide the coefficients 2. Subtract the exponents
6.74 x 10^-7
base

25. 0 to any power is equal to
Step 1. Divide the coefficients of the terms
same exponent
0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

26. When you change the position of the decimal point in a coefficient value
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
3
1. Divide the coefficients 2. Subtract the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.

27. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
1
cubed
Scientific notation

28. 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.
radical sign
decrease the value of the exponent by 1 (dividing by 10)
10^-18
10^1

29. When the exponents are not the same
0
rewrite one of the terms so that the exponents are equal
10^2
cubed

30. A number with an exponent of 2 is often said to be
10^1
squared
The solution exists - but not in the real number system.
Moving the decimal point to the right

31. A number with an exponent of 3 is often said to be
exponent
Not
When moving the decimal point to the left (dividing by 10)
cubed

32. Don't bother trying to find the square root of a negative number.
2
The solution exists - but not in the real number system.
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
Are Equal

33. 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.
exponent
perfect square
Engineering notation
0

34. For the 10
9 (3^2 = 9)
exponent
Moving the decimal point to the right
same exponent

35. There are no special rules for adding and subtracting numbers that are written with exponents.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
perfect square
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

36. To find the square root of any number - simply key in the number (the radicand) and press the
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Calculator square-root key
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
increase the power-of-10 exponent by the same number of units

37. The cube root of zero is
10^1
5
you have to adjust the value of the exponent in order avoid changing the actual value.
0

38. To subtract powers of ten:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
0
Subtract the exponent

39. 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.
exponent
Scientific notation
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
move the decimal point the same number of units to the right

40. 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
change both terms in order to keep the value the same.
negative number
decrease the power-of-10 exponent by the same number of units
square root

41. The square of 3 is
cube root
9 (3^2 = 9)
adjust the value of the coefficient
Same base

42. Indicates the number of times the base is to be multiplied.
The solution exists - but not in the real number system.
10^1
Because 4 multiplied by itself equals 16.
exponent

43. 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.
Moving the decimal point to the left
perfect square
a fractional decimal
Same base

44. 5^1 =
5
Scientific notation
0
1. Multiply the coefficients 2. Add the exponents

45. When you move the decimal point in the coefficient to the right
decrease the power-of-10 exponent by the same number of units
Engineering notation
3
move the decimal point the same number of units to the right

46. The square root of 9 is
proper scientific
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
1. Divide the coefficients 2. Subtract the exponents

47. Any number with an exponent of 0 is equal to
Same base
cube root
1
adjust the value of the coefficient

48. The symbol for the cube root of a number is
1
exponent
base
the radical sign with a little 3 that indicates the cube root:

49. To multiply powers of 10:
the radical sign with a little 3 that indicates the cube root:
Step 1. Divide the coefficients of the terms
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.
cubed

50. = 0.1 - or 1 with the decimal point moved one place to the left.
increase the power-of-10 exponent by the same number of units
10^-1
cube root
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