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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. For the 10
1 divided by that number with a positive exponent
Subtract the exponent
cube-root key
exponent

2. The square root of zero is
0
radical sign
increase the power-of-10 exponent by the same number of units
squared

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.
square root
radical sign
Moving the decimal point to the left
1. Divide the coefficients 2. Subtract the exponents

4. When the exponents are not the same
itself
radical sign
exponent
rewrite one of the terms so that the exponents are equal

5. 3^0 =
1
Same base
0
Engineering notation

6.
10^1
rewrite one of the terms so that the exponents are equal
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
Scientific notation

7. 1 to any power is equal to
Subtract the exponent
3
1
increase the power-of-10 exponent by the same number of units

8. Valid powers of 10 for engineering notation are:
0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

9. Dividing by 10
radical sign
exponent
Moving the decimal point to the left
same exponent

10. To add powers of ten:
cube root
10^-2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
coefficient

11. 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
Engineering notation
radical sign
0
adjust the value of the coefficient

12. To divide powers that have the same base:
0
coefficient
negative number
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

13. Always 10 for scientific notation
6.74 x 10^-7
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

14. 5^1 =
5
itself
When moving the decimal point to the left (dividing by 10)
cube root

15. Numbers with exponents can be directly multiplied or divided only when they have the
Same base
Step 1. Divide the coefficients of the terms
proper scientific
a fractional decimal

16. 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
the radical sign with a little 3 that indicates the cube root:
To multiply powers that have the same base:
change both terms in order to keep the value the same.
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. Multiplying by 10
1. Divide the coefficients 2. Subtract the exponents
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^1
Moving the decimal point to the right

18. 0^5 =
decrease the value of the exponent by 1 (dividing by 10)
you have to adjust the value of the exponent in order avoid changing the actual value.
0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

19. 100 - or 1 with the decimal point moved two places to the right
10^2
2
1 divided by that number with a positive exponent
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

20. Valid powers-of-10 for engineering notation
1. Divide the coefficients 2. Subtract the exponents
must be multiples of 3 or 0
1 divided by that number with a positive exponent
When moving the decimal point to the left (dividing by 10)

21. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
9 (3^2 = 9)
Moving the decimal point to the left

22. Indicates the number of times the base is to be multiplied.
6.74 x 10^-7
exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left

23. 10 - or 1 with the decimal point moved one place to the right
Engineering notation
10^1
square root
Not

24. To subtract powers of ten:
same exponent
1
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

25. Scientific notation requires there to be only
1 divided by that number with a positive exponent
one digit to the left of the decimal point
move the decimal point the same number of units to the right
1. Divide the coefficients 2. Subtract the exponents

26. 0 to any power is equal to
0
change both terms in order to keep the value the same.
Same base
3

27. 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
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
base
coefficient
same exponent

28. 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.
decrease the power-of-10 exponent by the same number of units
When the exponent of a power-of-10 expression is a negative integer:
Not
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.

29. Any number with an exponent of 1 is equal to
you have to adjust the value of the exponent in order avoid changing the actual value.
itself
1
rewrite one of the terms so that the exponents are equal

30. The cube root of zero is
3
0
Not
base

31. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
the radical sign with a little 3 that indicates the cube root:
10^-2
cube-root key

32. The square of 3 is
1
the radical sign with a little 3 that indicates the cube root:
Not
9 (3^2 = 9)

33. 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.
1
When moving the decimal point to the left (dividing by 10)
1 divided by that number with a positive exponent

34. When you move the decimal point in the coefficient to the left
5
cube root
1. Divide the coefficients 2. Subtract the exponents
increase the power-of-10 exponent by the same number of units

35. 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
10^1
decrease the value of the exponent by 1 (dividing by 10)

36. 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
square root
cube-root key
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0

37. Any number with an exponent of 0 is equal to
move the decimal point the same number of units to the right
Not
1
0

38. Any number with a negative exponent is equal to
increase the power-of-10 exponent by the same number of units
1 divided by that number with a positive exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
rewrite one of the terms so that the exponents are equal

39. 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.
1 divided by that number with a positive exponent
0
Engineering notation
The solution exists - but not in the real number system.

40. To multiply or divide exponent terms that do not have the same base:
0
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the right

41. To add or subtract numbers written with exponents:
Subtract the exponent
1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
same exponent

42. When you increase the value of the power-of-10 exponent
10^-1
adjust the value of the coefficient
rewrite one of the terms so that the exponents are equal
move the decimal point the same number of units to the left

43. A number with an exponent of 2 is often said to be
squared
increase the power-of-10 exponent by the same number of units
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

44. A number - when multiplied by itself - is equal to a given number.
move the decimal point the same number of units to the right
10^2
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
square root

45. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
a fractional decimal
perfect square
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

46. A very small number such as 0.000000674 can be written with scientific notation as
one digit to the left of the decimal point
When moving the decimal point to the left (dividing by 10)
6.74 x 10^-7
rewrite one of the terms so that the exponents are equal

47. Don't bother trying to find the square root of a negative number.
decrease the value of the exponent by 1 (dividing by 10)
The solution exists - but not in the real number system.
1. Divide the coefficients 2. Subtract the exponents
base

48. 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.
one digit to the left of the decimal point
5

49. 1 to any power is equal to
the radical sign with a little 3 that indicates the cube root:
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
same exponent

50. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Moving the decimal point to the left
Subtract the exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.