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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Indicates the number to be multiplied.
move the decimal point the same number of units to the left
When the exponent of a power-of-10 expression is a negative integer:
base
2 x 10^9

2. = 0.01 - or 1 with the decimal point moved two places to the left.
Because 4 multiplied by itself equals 16.
0
10^-2
cube-root key

3. The symbol for the cube root of a number is
square root
base
When the exponent of a power-of-10 expression is a negative integer:
the radical sign with a little 3 that indicates the cube root:

4. 3^0 =
Not
1
0
0

5. When you decrease the value of the power-of-10 exponent
square root
9 (3^2 = 9)
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.
move the decimal point the same number of units to the right

6. The cube root of a negative number is also a
negative number
10^-2
cubed
9 (3^2 = 9)

7. When you change the position of the decimal point in a coefficient value
Moving the decimal point to the right
adjust the value of the coefficient
a fractional decimal
you have to adjust the value of the exponent in order avoid changing the actual value.

8. The square root of zero is
0
Are Equal
perfect square
the radical sign with a little 3 that indicates the cube root:

9. 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.
coefficient
9 (3^2 = 9)
Scientific notation
When the exponent of a power-of-10 expression is a negative integer:

10. Any number with an exponent of 1 is equal to
itself
Engineering notation
one digit to the left of the decimal point
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

11. Indicates the number of times the base is to be multiplied.
10^-2
2
cube-root key
exponent

12. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
adjust the value of the coefficient
2 x 10^9
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

13. 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.
you have to adjust the value of the exponent in order avoid changing the actual value.
perfect square
cube-root key
same exponent

14. The decimal part
10^-18
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
coefficient
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

15. To add powers of ten:
1. Multiply the coefficients 2. Add the exponents
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0
increase the power-of-10 exponent by the same number of units

16. 10 - or 1 with the decimal point moved one place to the right
adjust the value of the coefficient
10^1
Engineering notation
base

17. 5^1 =
squared
5
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Same base

18. 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. Divide the coefficients 2. Subtract the exponents
9 (3^2 = 9)
change both terms in order to keep the value the same.
base

19. 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
10^-2
decrease the value of the exponent by 1 (dividing by 10)
square root
same exponent

20. The square root of 9 is
3
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. Subtract the coefficients 3. Assign the common power of ten
10^2

21. 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
1
adjust the value of the coefficient
Step 1. Divide the coefficients of the terms
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

22. Always 10 for scientific notation
1
base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1

23.
9 (3^2 = 9)
1 divided by that number with a positive exponent
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
base

24. 1 to any power is equal to
1. Multiply the coefficients 2. Add the exponents
The solution exists - but not in the real number system.
1
10^-2

25. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
negative number
Step 1. Divide the coefficients of the terms
cube-root key

26. The square of 3 is
9 (3^2 = 9)
1. Multiply the coefficients 2. Add the exponents
coefficient
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

27. Powers of ten can be added or subtracted only when their exponents
move the decimal point the same number of units to the left
increase the power-of-10 exponent by the same number of units
Are Equal
2

28. 0^5 =
0
perfect square
a fractional decimal
Moving the decimal point to the left

29. 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.
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
Engineering notation
Are Equal
The solution exists - but not in the real number system.

30. To divide powers of 10:
Step 1. Divide the coefficients of the terms
0
decrease the value of the exponent by 1 (dividing by 10)
3

31. Numbers with exponents can be directly multiplied or divided only when they have the
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.
a fractional decimal
2
Same base

32. A number with an exponent of 2 is often said to be
move the decimal point the same number of units to the right
squared
move the decimal point the same number of units to the left
adjust the value of the coefficient

33. What number multiplied by itself is equal to 16? The answer is 4. Why?
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
0
Because 4 multiplied by itself equals 16.
coefficient

34. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
negative number
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

35. Any number with an exponent of 0 is equal to
3
exponent
Step 1. Divide the coefficients of the terms
1

36. A very small number such as 0.000000674 can be written with scientific notation as
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
base
6.74 x 10^-7
squared

37. 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
Moving the decimal point to the left
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
2

38. 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.
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
Moving the decimal point to the left

39. To find the square root of any number - simply key in the number (the radicand) and press the
Calculator square-root key
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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. Multiply the coefficients 2. Add the exponents

40. Increase the value of the exponent by 1 (multiplying by 10)
Moving the decimal point to the left
Are Equal
When moving the decimal point to the left (dividing by 10)
0

41. 100 - or 1 with the decimal point moved two places to the right
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.
adjust the value of the coefficient
1
10^2

42. Dividing by 10
1
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left

43. To multiply powers of ten:
square root
Subtract the exponent
1. Multiply the coefficients 2. Add the exponents
10^2

44. When moving the decimal point to the right (multiplying by 10)
9 (3^2 = 9)
decrease the value of the exponent by 1 (dividing by 10)
a fractional decimal
1. Divide the coefficients 2. Subtract the exponents

45. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
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
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

46. Represents 1 preceded by 17 zeros and a decimal point.
1
10^-18
exponent
Not

47. To subtract powers of ten:
Moving the decimal point to the left
10^-2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
base

48. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
3
adjust the value of the coefficient
cube root

49. Valid powers of 10 for engineering notation are:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
a fractional decimal
you have to adjust the value of the exponent in order avoid changing the actual value.

50. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Scientific notation
proper scientific
Engineering notation
itself