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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. Always 10 for scientific notation
base
0
1
move the decimal point the same number of units to the left

2. A very small number such as 0.000000674 can be written with scientific notation as
one digit to the left of the decimal point
6.74 x 10^-7
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
decrease the power-of-10 exponent by the same number of units

3. Allows you to express very large and very small numbers without using large numbers of digits and decimal places. It's all done with powers of ten.
2
1
Same base
Scientific notation

4. When you move the decimal point in the coefficient to the right
cubed
10^-18
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:

5. 1 to any power is equal to
1
increase the power-of-10 exponent by the same number of units
0
perfect square

6. What number multiplied by itself is equal to 16? The answer is 4. Why?
9 (3^2 = 9)
the radical sign with a little 3 that indicates the cube root:
decrease the value of the exponent by 1 (dividing by 10)
Because 4 multiplied by itself equals 16.

7. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
cube-root key
proper scientific
When the exponent of a power-of-10 expression is a negative integer:
move the decimal point the same number of units to the left

8. Powers of ten can be added or subtracted only when their exponents
Are Equal
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.
Moving the decimal point to the right
same exponent

9. To multiply powers of ten:
cube root
rewrite one of the terms so that the exponents are equal
1. Multiply the coefficients 2. Add the exponents
5

10. 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.
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:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
decrease the power-of-10 exponent by the same number of units

11. Valid powers-of-10 for engineering notation
cubed
must be multiples of 3 or 0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
2

12. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
squared
itself
Not

13. The cube root of zero is
0
proper scientific
To multiply powers that have the same base:
When moving the decimal point to the left (dividing by 10)

14. 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
radical sign
0
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

15. = 0.1 - or 1 with the decimal point moved one place to the left.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
When moving the decimal point to the left (dividing by 10)
1
10^-1

16. Increase the value of the exponent by 1 (multiplying by 10)
Same base
10^1
0
When moving the decimal point to the left (dividing by 10)

17. A number is a second number which - when multiplied by itself three times - equals the original number.
1
cube root
9 (3^2 = 9)
0

18. When you decrease the value of the power-of-10 exponent
cubed
perfect square
move the decimal point the same number of units to the right
cube root

19. To multiply powers of 10:
Subtract the exponent
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.
Because 4 multiplied by itself equals 16.

20. Indicates the number of times the base is to be multiplied.
10^2
perfect square
Calculator square-root key
exponent

21. For the 10
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
squared
exponent
decrease the value of the exponent by 1 (dividing by 10)

22. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
proper scientific
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
exponent

23. Scientific notation requires there to be only
decrease the power-of-10 exponent by the same number of units
one digit to the left of the decimal point
0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

24. Dividing by 10
The solution exists - but not in the real number system.
adjust the value of the coefficient
Moving the decimal point to the left
Because 4 multiplied by itself equals 16.

25. To add powers of ten:
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
0
cube-root key

26. To find the square root of any number - simply key in the number (the radicand) and press the
1. Multiply the coefficients 2. Add the exponents
decrease the power-of-10 exponent by the same number of units
1. Divide the coefficients 2. Subtract the exponents
Calculator square-root key

27. To subtract powers of ten:
base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Are Equal
cubed

28. There are no special rules for adding and subtracting numbers that are written with exponents.
Calculator square-root key
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
adjust the value of the coefficient
To multiply powers that have the same base:

29. Step 1: Add the exponents Step 2: Use the common base
9 (3^2 = 9)
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
To multiply powers that have the same base:
1. Divide the coefficients 2. Subtract the exponents

30. The square root of zero is
1
10^-2
adjust the value of the coefficient
0

31. Numbers with exponents can be directly multiplied or divided only when they have the
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
1
1

32. 0^5 =
move the decimal point the same number of units to the left
cube-root key
exponent
0

33. Indicates the number to be multiplied.
base
10^-18
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
one digit to the left of the decimal point

34. Any number with a negative exponent is equal to
exponent
Moving the decimal point 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
1 divided by that number with a positive exponent

35. Any number with an exponent of 0 is equal to
9 (3^2 = 9)
exponent
1
decrease the power-of-10 exponent by the same number of units

36. 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.
1. Divide the coefficients 2. Subtract the exponents
move the decimal point the same number of units to the left
perfect square
adjust the value of the coefficient

37. When you change the position of the decimal point in a coefficient value
1
1. Divide the coefficients 2. Subtract the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

38. Any number with an exponent of 1 is equal to
proper scientific
itself
cube root
exponent

39. = 0.01 - or 1 with the decimal point moved two places to the left.
Subtract the exponent
10^-2
Scientific notation
1

40. To divide powers that have the same base:
Moving the decimal point 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
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

41. To divide powers of 10:
Step 1. Divide the coefficients of the terms
0
5
cube root

42. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
a fractional decimal
To multiply powers that have the same base:

43. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
1 divided by that number with a positive exponent
coefficient
3

44. 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
square root
base
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

45. The decimal part
coefficient
Not
Step 1. Divide the coefficients of the terms
1. Divide the coefficients 2. Subtract the exponents

46. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Calculator square-root key

47. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
perfect square
Same base
9 (3^2 = 9)
Subtract the exponent

48. Negative cube roots are okay ... negative square roots are
exponent
Step 1. Divide the coefficients of the terms
Not
2 x 10^9

49. To multiply or divide exponent terms that do not have the same base:
adjust the value of the coefficient
proper scientific
Scientific notation
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

50. A number with an exponent of 2 is often said to be
10^1
Not
squared
decrease the power-of-10 exponent by the same number of units