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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 add or subtract numbers written with exponents:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Calculator square-root key
move the decimal point the same number of units to the right

2. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
5
Are Equal
exponent

3. 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.
radical sign
10^1
When moving the decimal point to the left (dividing by 10)
Are Equal

4. The square root of 9 is
one digit to the left of the decimal point
0
6.74 x 10^-7
3

5. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
10^2
6.74 x 10^-7
Scientific notation

6. 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
same exponent
1
2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

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
move the decimal point the same number of units to the left
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^1

8. Step 1: Add the exponents Step 2: Use the common base
move the decimal point the same number of units to the right
To multiply powers that have the same base:
10^1
decrease the power-of-10 exponent by the same number of units

9. To divide powers of 10:
0
Step 1. Divide the coefficients of the terms
square root
Calculator square-root key

10. 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.
increase the power-of-10 exponent by the same number of units
When the exponent of a power-of-10 expression is a negative integer:
perfect square
Subtract the exponent

11. The symbol for the cube root of a number is
0
Moving the decimal point to the right
proper scientific
the radical sign with a little 3 that indicates the cube root:

12. Any number with an exponent of 1 is equal to
itself
10^1
1
1. Divide the coefficients 2. Subtract the exponents

13. 100 - or 1 with the decimal point moved two places to the right
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
change both terms in order to keep the value the same.
10^2
perfect square

14. Dividing by 10
adjust the value of the coefficient
Moving the decimal point to the left
Scientific notation
Subtract the exponent

15. To multiply or divide exponent terms that do not have the same base:
The solution exists - but not in the real number system.
10^-2
Moving the decimal point to the left
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

16. To multiply powers of 10:
Scientific notation
3
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.

17. To divide powers that have the same base:
change both terms in order to keep the value the same.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Because 4 multiplied by itself equals 16.
1

18. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
5
increase the power-of-10 exponent by the same number of units

19. The cube root of zero is
The solution exists - but not in the real number system.
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.
the radical sign with a little 3 that indicates the cube root:

20. The square of 3 is
cubed
adjust the value of the coefficient
9 (3^2 = 9)
To multiply powers that have the same base:

21. 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
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
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.

22. To add powers of ten:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
6.74 x 10^-7
The solution exists - but not in the real number system.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

23. Valid powers of 10 for engineering notation are:
one digit to the left of the decimal point
Not
same exponent
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

24. When you move the decimal point in the coefficient to the left
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
proper scientific
increase the power-of-10 exponent by the same number of units
3

25. 3^0 =
Not
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
you have to adjust the value of the exponent in order avoid changing the actual value.

26. When moving the decimal point to the right (multiplying by 10)
base
2 x 10^9
decrease the value of the exponent by 1 (dividing by 10)
move the decimal point the same number of units to the left

27. Don't bother trying to find the square root of a negative number.
1
The solution exists - but not in the real number system.
Moving the decimal point to the right
must be multiples of 3 or 0

28. 1 to any power is equal to
base
1
Not
Scientific notation

29. When you move the decimal point in the coefficient to the right
increase the power-of-10 exponent by the same number of units
decrease the power-of-10 exponent by the same number of units
9 (3^2 = 9)
Moving the decimal point to the right

30. Numbers with exponents can be directly multiplied or divided only when they have the
1. Divide the coefficients 2. Subtract the exponents
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1 divided by that number with a positive exponent
Same base

31. The decimal part
1
move the decimal point the same number of units to the left
9 (3^2 = 9)
coefficient

32. 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:
Are Equal
cubed
Engineering notation

33. 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
Step 1. Divide the coefficients of the terms
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:
change both terms in order to keep the value the same.

34. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
1
coefficient
2

35. Powers of ten can be added or subtracted only when their exponents
Are Equal
Not
The solution exists - but not in the real number system.
10^-2

36. The square root of zero is
0
Scientific notation
6.74 x 10^-7
10^-1

37. There are no special rules for adding and subtracting numbers that are written with exponents.
0
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:
10^1

38. 1^4 =
Calculator square-root key
1
adjust the value of the coefficient
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.

39. For the 10
Step 1. Divide the coefficients of the terms
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.
Not
exponent

40. Scientific notation requires there to be only
The solution exists - but not in the real number system.
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
Because 4 multiplied by itself equals 16.

41. 0 to any power is equal to
1
change both terms in order to keep the value the same.
Not
0

42. 1 to any power is equal to
decrease the power-of-10 exponent by the same number of units
3
1
base

43. Always 10 for scientific notation
Are Equal
base
coefficient
1

44. A negative exponent does not mean the decimal value is negative. It means the decimal value is
3
Moving the decimal point to the right
a fractional decimal
To multiply powers that have the same base:

45. 5^1 =
5
10^1
1
10^-1

46. Valid powers-of-10 for engineering notation
1 divided by that number with a positive exponent
The solution exists - but not in the real number system.
must be multiples of 3 or 0
rewrite one of the terms so that the exponents are equal

47. Any number with a negative exponent is equal to
decrease the power-of-10 exponent by the same number of units
square root
1 divided by that number with a positive exponent
coefficient

48. Multiplying by 10
Because 4 multiplied by itself equals 16.
1
Moving the decimal point to the right
0

49. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
0
cube-root key
itself

50. When you change the position of the decimal point in a coefficient value
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left
you have to adjust the value of the exponent in order avoid changing the actual value.
2 x 10^9