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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 that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
cube root

2. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
move the decimal point the same number of units to the left
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^1

3. 3^0 =
1
0
cube-root key
Are Equal

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

5. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
10^1
9 (3^2 = 9)
2
6.74 x 10^-7

6. The cube root of zero is
proper scientific
0
cubed
itself

7. There are no special rules for adding and subtracting numbers that are written with exponents.
base
6.74 x 10^-7
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

8. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
base
9 (3^2 = 9)
1
proper scientific

9. To add or subtract numbers written with exponents:
move the decimal point the same number of units to the left
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
one digit to the left of the decimal point
Step 1. Divide the coefficients of the terms

10. 10 - or 1 with the decimal point moved one place to the right
10^1
1
cube root
5

11. A number with an exponent of 3 is often said to be
negative number
Moving the decimal point to the left
cubed
0

12. 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.
Engineering notation
radical sign
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1

13. To find the square root of any number - simply key in the number (the radicand) and press the
Scientific notation
Calculator square-root key
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. Divide the coefficients of the terms

14. To multiply powers of ten:
adjust the value of the coefficient
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1. Multiply the coefficients 2. Add the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.

15. Any number with an exponent of 1 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
decrease the power-of-10 exponent by the same number of units
1. Multiply the coefficients 2. Add the exponents
itself

16. The decimal part
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
coefficient
cubed
Calculator square-root key

17. The symbol for the cube root of a number is
5
the radical sign with a little 3 that indicates the cube root:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
The solution exists - but not in the real number system.

18. Powers of ten can be added or subtracted only when their exponents
adjust the value of the coefficient
Are Equal
must be multiples of 3 or 0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

19. 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
Engineering notation
6.74 x 10^-7
perfect square
cube-root key

20. Valid powers-of-10 for engineering notation
cube-root key
Engineering notation
adjust the value of the coefficient
must be multiples of 3 or 0

21. Negative cube roots are okay ... negative square roots are
exponent
0
Not
Same base

22. A negative exponent does not mean the decimal value is negative. It means the decimal value is
1. Multiply the coefficients 2. Add the exponents
When moving the decimal point to the left (dividing by 10)
a fractional decimal
0

23. Scientific notation requires there to be only
Step 1. Divide the coefficients of the terms
negative number
one digit to the left of the decimal point
Are Equal

24.
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^-2
a fractional decimal
adjust the value of the coefficient

25. 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
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.
same exponent
change both terms in order to keep the value the same.

26. Indicates the number of times the base is to be multiplied.
Step 1. Divide the coefficients of the terms
exponent
1. Multiply the coefficients 2. Add the exponents
1

27. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
cubed
proper scientific
2 x 10^9
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

28. To add powers of ten:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1. Multiply the coefficients 2. Add the exponents
0
base

29. Increase the value of the exponent by 1 (multiplying by 10)
negative number
6.74 x 10^-7
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
When moving the decimal point to the left (dividing by 10)

30. The square root of zero is
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
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

31. 1 to any power is equal to
1
1. Multiply the coefficients 2. Add the exponents
10^2
3

32. To divide powers that have the same base:
radical sign
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^1

33. = 0.1 - or 1 with the decimal point moved one place to the left.
1
squared
10^-1
perfect square

34. 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
9 (3^2 = 9)
adjust the value of the coefficient
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

35. When you decrease the value of the power-of-10 exponent
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
one digit to the left of the decimal point
move the decimal point the same number of units to the right
0

36. 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
1
move the decimal point the same number of units to the left
proper scientific

37. = 0.01 - or 1 with the decimal point moved two places to the left.
proper scientific
cubed
10^-2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

38. The square of 3 is
9 (3^2 = 9)
the radical sign with a little 3 that indicates the cube root:
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.
Are Equal

39. Dividing by 10
itself
Moving the decimal point to the left
coefficient
0

40. A very small number such as 0.000000674 can be written with scientific notation as
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the right
3
6.74 x 10^-7

41. Valid powers of 10 for engineering notation are:
perfect square
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1
10^-1

42. 5^1 =
Are Equal
Calculator square-root key
5
0

43. 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
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
change both terms in order to keep the value the same.
proper scientific
Not

44. 0 to any power is equal to
Moving the decimal point to the left
coefficient
base
0

45. 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.
must be multiples of 3 or 0
Scientific notation
2 x 10^9
When the exponent of a power-of-10 expression is a negative integer:

46. Numbers with exponents can be directly multiplied or divided only when they have the
must be multiples of 3 or 0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
When moving the decimal point to the left (dividing by 10)
Same base

47. To multiply powers of 10:
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.
squared
square root
itself

48. 1^4 =
move the decimal point the same number of units to the right
0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1

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

50. 1 to any power is equal to
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
5
1
coefficient