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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. 1^4 =
1
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 x 10^9

2. A negative exponent does not mean the decimal value is negative. It means the decimal value is
move the decimal point the same number of units to the left
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
a fractional decimal
radical sign

3. What number multiplied by itself is equal to 16? The answer is 4. Why?
9 (3^2 = 9)
1
Because 4 multiplied by itself equals 16.
increase the power-of-10 exponent by the same number of units

4. Multiplying by 10
cube-root key
squared
radical sign
Moving the decimal point to the right

5. A number with an exponent of 3 is often said to be
cubed
10^2
0
squared

6. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
adjust the value of the coefficient
the radical sign with a little 3 that indicates the cube root:
5
2

7. Powers of ten can be added or subtracted only when their exponents
rewrite one of the terms so that the exponents are equal
The solution exists - but not in the real number system.
2 x 10^9
Are Equal

8. Represents 1 preceded by 17 zeros and a decimal point.
move the decimal point the same number of units to the left
3
10^-18
When the exponent of a power-of-10 expression is a negative integer:

9. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
9 (3^2 = 9)
Moving the decimal point 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

10. Don't bother trying to find the square root of a negative number.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^-1
move the decimal point the same number of units to the left
The solution exists - but not in the real number system.

11. To divide powers that have the same base:
1 divided by that number with a positive exponent
perfect square
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Step 1. Divide the coefficients of the terms

12. The square of 3 is
Scientific notation
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
9 (3^2 = 9)
10^1

13. 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
The solution exists - but not in the real number system.
proper scientific

14. 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.
move the decimal point the same number of units to the right
Engineering notation
exponent
itself

15. To add powers of ten:
1
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

16. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
The solution exists - but not in the real number system.
the radical sign with a little 3 that indicates the cube root:

17. To find the square root of any number - simply key in the number (the radicand) and press the
squared
Calculator square-root key
0
base

18. For the 10
10^2
must be multiples of 3 or 0
exponent
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

19. The square root of 9 is
0
cube-root key
3
1

20. When you move the decimal point in the coefficient to the right
change both terms in order to keep the value the same.
move the decimal point the same number of units to the left
decrease the power-of-10 exponent by the same number of units
Subtract the exponent

21.
cube root
square 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
Not

22. 3^0 =
negative number
The solution exists - but not in the real number system.
radical sign
1

23. 0 to any power is equal to
6.74 x 10^-7
Calculator square-root key
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0

24. When you move the decimal point in the coefficient to the left
10^-2
The solution exists - but not in the real number system.
move the decimal point the same number of units to the right
increase the power-of-10 exponent by the same number of units

25. Indicates the number to be multiplied.
change both terms in order to keep the value the same.
When the exponent of a power-of-10 expression is a negative integer:
base
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

26. There are no special rules for adding and subtracting numbers that are written with exponents.
1. Multiply the coefficients 2. Add the exponents
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

27. Scientific notation requires there to be only
one digit to the left of the decimal point
Step 1. Divide the coefficients of the terms
0
squared

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

29. The cube root of zero is
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
0
1

30. 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.
perfect square
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
base
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

31. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-2
Engineering notation
10^-1
Scientific notation

32. Valid powers of 10 for engineering notation are:
Engineering notation
you have to adjust the value of the exponent in order avoid changing the actual value.
9 (3^2 = 9)
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

33. 0^5 =
must be multiples of 3 or 0
Are Equal
Moving the decimal point to the right
0

34. Dividing by 10
Moving the decimal point to the left
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
itself
1 divided by that number with a positive exponent

35. 10 - or 1 with the decimal point moved one place to the right
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
cubed
When the exponent of a power-of-10 expression is a negative integer:
10^1

36. 5^1 =
radical sign
Calculator square-root key
Moving the decimal point to the left
5

37. To multiply powers of 10:
0
a fractional decimal
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.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

38. The decimal part
square root
The solution exists - but not in the real number system.
9 (3^2 = 9)
coefficient

39. Increase the value of the exponent by 1 (multiplying by 10)
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
When moving the decimal point to the left (dividing by 10)
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

40. 1 to any power is equal to
decrease the power-of-10 exponent by the same number of units
1
Subtract the exponent
itself

41. Any number with an exponent of 1 is equal to
1. Divide the coefficients 2. Subtract the exponents
rewrite one of the terms so that the exponents are equal
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
itself

42. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
square root
2 x 10^9
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0

43. Indicates the number of times the base is to be multiplied.
1. Divide the coefficients 2. Subtract the exponents
exponent
adjust the value of the coefficient
Same base

44. When moving the decimal point to the right (multiplying by 10)
Same base
decrease the value of the exponent by 1 (dividing by 10)
rewrite one of the terms so that the exponents are equal
Not

45. To add or subtract numbers written with exponents:
must be multiples of 3 or 0
1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Not

46. 1 to any power is equal to
1
decrease the value of the exponent by 1 (dividing by 10)
a fractional decimal
Not

47. 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
1
move the decimal point the same number of units to the left
coefficient

48. Always 10 for scientific notation
To multiply powers that have the same base:
2 x 10^9
base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

49. Any number with a negative exponent is equal to
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
When the exponent of a power-of-10 expression is a negative integer:
1 divided by that number with a positive exponent
1

50. When you increase the value of the power-of-10 exponent
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
2
move the decimal point the same number of units to the left
10^1

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CLEP General Mathematics: Powers Exponents And Roots

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