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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. Valid powers-of-10 for engineering notation
When moving the decimal point to the left (dividing by 10)
increase the power-of-10 exponent by the same number of units
0
must be multiples of 3 or 0

2. 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
Engineering notation
Moving the decimal point to the left

3. A number is a second number which - when multiplied by itself three times - equals the original number.
same exponent
cube root
0
1 divided by that number with a positive exponent

4. To divide powers that have the same base:
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:
10^-2
10^-18

5. 0^5 =
the radical sign with a little 3 that indicates the cube root:
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.
0
1

6. 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
negative number
To multiply powers that have the same base:
10^2

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

8. The square root of 9 is
3
6.74 x 10^-7
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
squared

9. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
10^-18
same exponent
Scientific notation

10. 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.
cube-root key
0
decrease the value of the exponent by 1 (dividing by 10)

11. 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.
10^2
Scientific notation
1
5

12. The cube root of a negative number is also a
base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
perfect square
negative number

13. Always 10 for scientific notation
base
10^1
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.

14. To divide powers of ten:
squared
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
5
1. Divide the coefficients 2. Subtract the exponents

15. Represents 1 preceded by 17 zeros and a decimal point.
move the decimal point the same number of units to the left
10^-18
1
Scientific notation

16. Don't bother trying to find the square root of a negative number.
exponent
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
The solution exists - but not in the real number system.
squared

17. 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
0
squared
cube-root key
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.

18. To subtract powers of ten:
adjust the value of the coefficient
1 divided by that number with a positive exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Not

19. 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.
perfect square
radical sign
adjust the value of the coefficient
a fractional decimal

20. To multiply powers of 10:
2 x 10^9
Scientific notation
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.

21. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
1. Divide the coefficients 2. Subtract the exponents
When moving the decimal point to the left (dividing by 10)
2 x 10^9
rewrite one of the terms so that the exponents are equal

22. A negative exponent does not mean the decimal value is negative. It means the decimal value is
10^-1
Subtract the exponent
a fractional decimal
must be multiples of 3 or 0

23. For the 10
10^-18
Not
Engineering notation
exponent

24. When you decrease the value of the power-of-10 exponent
a fractional decimal
2 x 10^9
the radical sign with a little 3 that indicates the cube root:
move the decimal point the same number of units to the right

25. A number - when multiplied by itself - is equal to a given number.
Engineering notation
exponent
square root
negative number

26. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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
0
When the exponent of a power-of-10 expression is a negative integer:

27. When you move the decimal point in the coefficient to the right
3
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
negative number
decrease the power-of-10 exponent by the same number of units

28. The square of 3 is
coefficient
cube-root key
move the decimal point the same number of units to the right
9 (3^2 = 9)

29. 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
10^-18
0
proper scientific
change both terms in order to keep the value the same.

30. Any number with an exponent of 0 is equal to
cube-root key
square root
1
10^1

31. When you move the decimal point in the coefficient to the left
a fractional decimal
0
1. Multiply the coefficients 2. Add the exponents
increase the power-of-10 exponent by the same number of units

32. 0 to any power is equal to
The solution exists - but not in the real number system.
0
10^-18
a fractional decimal

33. Any number with an exponent of 1 is equal to
Because 4 multiplied by itself equals 16.
itself
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
exponent

34. What number multiplied by itself is equal to 16? The answer is 4. Why?
1
Because 4 multiplied by itself equals 16.
exponent
When the exponent of a power-of-10 expression is a negative integer:

35. When the exponents are not the same
Moving the decimal point to the right
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
Because 4 multiplied by itself equals 16.

36. Indicates the number to be multiplied.
3
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
base

37. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Not
Scientific notation
square root

38. A number with an exponent of 2 is often said to be
exponent
squared
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-2

39. 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.
perfect square
1. Multiply the coefficients 2. Add the exponents
2
move the decimal point the same number of units to the right

40. Multiplying by 10
move the decimal point the same number of units to the right
1. Divide the coefficients 2. Subtract the exponents
Moving the decimal point to the right
base

41. The square root of zero is
0
1
decrease the power-of-10 exponent by the same number of units
10^1

42.
adjust the value of the coefficient
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
change both terms in order to keep the value the same.
Same base

43. Numbers with exponents can be directly multiplied or divided only when they have the
Same base
the radical sign with a little 3 that indicates the cube root:
itself
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

44. = 0.1 - or 1 with the decimal point moved one place to the left.
1 divided by that number with a positive exponent
Step 1. Divide the coefficients of the terms
10^-1
1

45. 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.
10^-1
Same base
Engineering notation
Subtract the exponent

46. When you change the position of the decimal point in a coefficient value
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
The solution exists - but not in the real number system.
move the decimal point the same number of units to the left
you have to adjust the value of the exponent in order avoid changing the actual value.

47. Negative cube roots are okay ... negative square roots are
adjust the value of the coefficient
3
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

48. The decimal part
10^1
6.74 x 10^-7
coefficient
cube-root key

49. 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:
1
1
itself

50. 3^0 =
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
move the decimal point the same number of units to the right
coefficient
1