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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. To subtract powers of ten:
decrease the value of the exponent by 1 (dividing by 10)
same exponent
the radical sign with a little 3 that indicates the cube root:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

2. The square root of 9 is
Scientific notation
2
3
10^-1

3. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
The solution exists - but not in the real number system.
rewrite one of the terms so that the exponents are equal
9 (3^2 = 9)

4. To divide powers of 10:
10^-2
base
base
Step 1. Divide the coefficients of the terms

5.
0
1
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
Because 4 multiplied by itself equals 16.

6. Indicates the number to be multiplied.
base
cubed
The solution exists - but not in the real number system.
0

7. To add powers of ten:
9 (3^2 = 9)
When moving the decimal point to the left (dividing by 10)
Same base
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

8. There are no special rules for adding and subtracting numbers that are written with exponents.
Because 4 multiplied by itself equals 16.
coefficient
Same base
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

9. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
you have to adjust the value of the exponent in order avoid changing the actual value.
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
5

10. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
same exponent
Subtract the exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
2

11. When you move the decimal point in the coefficient to the right
base
perfect square
coefficient
decrease the power-of-10 exponent by the same number of units

12. To multiply powers of ten:
Moving the decimal point to the right
decrease the value of the exponent by 1 (dividing by 10)
6.74 x 10^-7
1. Multiply the coefficients 2. Add the exponents

13. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
6.74 x 10^-7
base
must be multiples of 3 or 0

14. Powers of ten can be added or subtracted only when their exponents
To multiply powers that have the same base:
Moving the decimal point to the right
2
Are Equal

15. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
The solution exists - but not in the real number system.
Subtract the exponent
proper scientific
perfect square

16. To multiply or divide exponent terms that do not have the same base:
1
1 divided by that number with a positive exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
cube-root key

17. Step 1: Add the exponents Step 2: Use the common base
a fractional decimal
When the exponent of a power-of-10 expression is a negative integer:
proper scientific
To multiply powers that have the same base:

18. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
10^1
a fractional decimal
The solution exists - but not in the real number system.

19. A number with an exponent of 3 is often said to be
the radical sign with a little 3 that indicates the cube root:
10^2
cubed
3

20. 100 - or 1 with the decimal point moved two places to the right
Because 4 multiplied by itself equals 16.
decrease the value of the exponent by 1 (dividing by 10)
1
10^2

21. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
exponent
Are Equal
10^-18

22. Any number with an exponent of 1 is equal to
itself
2 x 10^9
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.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

23. 1 to any power is equal to
Engineering notation
10^2
must be multiples of 3 or 0
1

24. To find the square root of any number - simply key in the number (the radicand) and press the
Calculator square-root key
10^-18
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

25. The decimal part
the radical sign with a little 3 that indicates the cube root:
coefficient
decrease the power-of-10 exponent by the same number of units
cube-root key

26. Always 10 for scientific notation
base
move the decimal point the same number of units to the right
move the decimal point the same number of units to the left
rewrite one of the terms so that the exponents are equal

27. The square root of zero is
0
you have to adjust the value of the exponent in order avoid changing the actual value.
base
radical sign

28. When moving the decimal point to the right (multiplying by 10)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left
decrease the value of the exponent by 1 (dividing by 10)
1. Divide the coefficients 2. Subtract the exponents

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.
adjust the value of the coefficient
decrease the power-of-10 exponent by the same number of units
Engineering notation
When moving the decimal point to the left (dividing by 10)

30. 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.
When the exponent of a power-of-10 expression is a negative integer:
10^1
proper scientific
decrease the power-of-10 exponent by the same number of units

31. Dividing 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
cube root
Moving the decimal point to the left
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.

32. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
1
radical sign
To multiply powers that have the same base:

33. 1^4 =
Not
1
cube-root key
When the exponent of a power-of-10 expression is a negative integer:

34. 3^0 =
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
squared
a fractional decimal

35. When you decrease the value of the power-of-10 exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
perfect square
move the decimal point the same number of units to the right
0

36. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
1. Divide the coefficients 2. Subtract the exponents
9 (3^2 = 9)
0

37. 0 to any power is equal to
0
itself
Moving the decimal point to the right
decrease the power-of-10 exponent by the same number of units

38. Numbers with exponents can be directly multiplied or divided only when they have the
1
Engineering notation
Same base
2

39. Don't bother trying to find the square root of a negative number.
cube root
The solution exists - but not in the real number system.
rewrite one of the terms so that the exponents are equal
10^-2

40. To divide powers that have the same base:
Scientific notation
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
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.
1

41. The cube root of zero is
1. Divide the coefficients 2. Subtract the exponents
1 divided by that number with a positive exponent
0
Moving the decimal point to the left

42. 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.
0
perfect square
2 x 10^9
10^-1

43. 5^1 =
1
Engineering notation
5
1

44. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
10^-2
The solution exists - but not in the real number system.
1. Divide the coefficients 2. Subtract the exponents

45. The square of 3 is
When moving the decimal point to the left (dividing by 10)
decrease the value of the exponent by 1 (dividing by 10)
9 (3^2 = 9)
10^-1

46. Multiplying by 10
0
square root
Moving the decimal point to the right
proper scientific

47. 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.
rewrite one of the terms so that the exponents are equal
10^2
same exponent

48. Any number with an exponent of 0 is equal to
To multiply powers that have the same base:
1
base
must be multiples of 3 or 0

49. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
5
decrease the value of the exponent by 1 (dividing 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

50. For the 10
Not
exponent
square root
Subtract the exponent