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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. 10 - or 1 with the decimal point moved one place to the right
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
Same base
10^1
move the decimal point the same number of units to the right

2. For the 10
1
must be multiples of 3 or 0
3
exponent

3. The square root of zero is
1
When the exponent of a power-of-10 expression is a negative integer:
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.

4. There are no special rules for adding and subtracting numbers that are written with exponents.
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
To multiply powers that have the same base:
rewrite one of the terms so that the exponents are equal

5. 100 - or 1 with the decimal point moved two places to the right
must be multiples of 3 or 0
To multiply powers that have the same base:
10^2
2

6. A very small number such as 0.000000674 can be written with scientific notation as
5
cube root
3
6.74 x 10^-7

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

8. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1
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
2

9. The cube root of zero is
0
Are Equal
the radical sign with a little 3 that indicates the cube root:
10^-1

10. The symbol for the cube root of a number is
Scientific notation
2
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
the radical sign with a little 3 that indicates the cube root:

11. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
0
proper scientific
1. Multiply the coefficients 2. Add the exponents
Because 4 multiplied by itself equals 16.

12. 0 to any power is equal to
decrease the value of the exponent by 1 (dividing by 10)
0
must be multiples of 3 or 0
10^-2

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.
squared
perfect square
Moving the decimal point to the left
1

14. When you move the decimal point in the coefficient to the left
0
the radical sign with a little 3 that indicates the cube root:
increase the power-of-10 exponent by the same number of units
adjust the value of the coefficient

15. Multiplying by 10
When the exponent of a power-of-10 expression is a negative integer:
Moving the decimal point to the right
move the decimal point the same number of units to the right
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

16. To find the square root of any number - simply key in the number (the radicand) and press the
a fractional decimal
Calculator square-root key
square root
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

17. To divide powers of 10:
Step 1. Divide the coefficients of the terms
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
change both terms in order to keep the value the same.
10^-2

18. A number with an exponent of 3 is often said to be
When the exponent of a power-of-10 expression is a negative integer:
cubed
one digit to the left of the decimal point
10^-2

19. Dividing by 10
Because 4 multiplied by itself equals 16.
must be multiples of 3 or 0
Moving the decimal point to the left
adjust the value of the coefficient

20. 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
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
square root
1

21. Increase the value of the exponent by 1 (multiplying by 10)
base
change both terms in order to keep the value the same.
Not
When moving the decimal point to the left (dividing by 10)

22. A number - when multiplied by itself - is equal to a given number.
square root
cube root
1
Scientific notation

23. The cube root of a negative number is also a
negative number
When the exponent of a power-of-10 expression is a negative integer:
9 (3^2 = 9)
1

24. Don't bother trying to find the square root of a negative number.
Because 4 multiplied by itself equals 16.
1 divided by that number with a positive exponent
The solution exists - but not in the real number system.
0

25. 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
Are Equal
6.74 x 10^-7
0

26. To divide powers that have the same base:
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
decrease the value of the exponent by 1 (dividing by 10)
one digit to the left of the decimal point

27. Always 10 for scientific notation
2 x 10^9
0
Same base
base

28. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
exponent
Engineering notation
5

29. Indicates the number to be multiplied.
Scientific notation
The solution exists - but not in the real number system.
base
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

30. 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
you have to adjust the value of the exponent in order avoid changing the actual value.
same exponent
move the decimal point the same number of units to the right
When the exponent of a power-of-10 expression is a negative integer:

31. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Are Equal
0
2 x 10^9
10^2

32. 1^4 =
Moving the decimal point to the right
0
1
the radical sign with a little 3 that indicates the cube root:

33. To divide powers of ten:
0
Same base
1. Divide the coefficients 2. Subtract the exponents
move the decimal point the same number of units to the left

34. Represents 1 preceded by 17 zeros and a decimal point.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
the radical sign with a little 3 that indicates the cube root:
exponent
10^-18

35. The square root of 9 is
cube-root key
The solution exists - but not in the real number system.
3
radical sign

36. Any number with an exponent of 0 is equal to
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Same base
When moving the decimal point to the left (dividing by 10)
1

37. 1 to any power is equal to
When the exponent of a power-of-10 expression is a negative integer:
change both terms in order to keep the value the same.
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.

38. 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.
base
When the exponent of a power-of-10 expression is a negative integer:
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
The solution exists - but not in the real number system.

39. When you change the position of the decimal point in a coefficient value
0
you have to adjust the value of the exponent in order avoid changing the actual value.
decrease the power-of-10 exponent by the same number of units
same exponent

40. 1 to any power is equal to
1
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.

41. When moving the decimal point to the right (multiplying by 10)
10^2
Step 1. Divide the coefficients of the terms
one digit to the left of the decimal point
decrease the value of the exponent by 1 (dividing by 10)

42. The decimal part
rewrite one of the terms so that the exponents are equal
coefficient
exponent
2 x 10^9

43. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
squared
Same base
increase the power-of-10 exponent by the same number of units

44. Valid powers-of-10 for engineering notation
10^2
5
must be multiples of 3 or 0
Because 4 multiplied by itself equals 16.

45. 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
same exponent
negative number
change both terms in order to keep the value the same.

46. A number is a second number which - when multiplied by itself three times - equals the original number.
10^2
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.
cube root
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

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

48. Scientific notation requires there to be only
one digit to the left of the decimal point
10^-18
1. Divide the coefficients 2. Subtract the 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

49. 5^1 =
adjust the value of the coefficient
Are Equal
5
proper scientific

50. 3^0 =
Are Equal
Scientific notation
1
base