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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. To multiply powers of ten:
5
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.
1. Multiply the coefficients 2. Add the exponents

2. The square root of 9 is
coefficient
move the decimal point the same number of units to the right
To multiply powers that have the same base:
3

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.
1 divided by that number with a positive exponent
radical sign
0
1

4. Multiplying by 10
Scientific notation
When the exponent of a power-of-10 expression is a negative integer:
Moving the decimal point to the right
must be multiples of 3 or 0

5. To divide powers of 10:
Step 1. Divide the coefficients of the terms
must be multiples of 3 or 0
Calculator square-root key
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

6. Indicates the number of times the base is to be multiplied.
0
radical sign
proper scientific
exponent

7. = 0.1 - or 1 with the decimal point moved one place to the left.
same exponent
When the exponent of a power-of-10 expression is a negative integer:
10^-1
1 divided by that number with a positive exponent

8. When the exponents are not the same
10^-2
1
rewrite one of the terms so that the exponents are equal
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

9. Indicates the number to be multiplied.
base
coefficient
To multiply powers that have the same base:
cubed

10. When moving the decimal point to the right (multiplying by 10)
Same base
decrease the value of the exponent by 1 (dividing by 10)
When the exponent of a power-of-10 expression is a negative integer:
Calculator square-root key

11. 0^5 =
Subtract the exponent
1
Same base
0

12. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
move the decimal point the same number of units to the left
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
6.74 x 10^-7

13. To add powers of ten:
Not
decrease the value of the exponent by 1 (dividing by 10)
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the left

14. There are no special rules for adding and subtracting numbers that are written with exponents.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
0
base
Not

15. Don't bother trying to find the square root of a negative number.
Engineering notation
1
proper scientific
The solution exists - but not in the real number system.

16. 10 - or 1 with the decimal point moved one place to the right
must be multiples of 3 or 0
change both terms in order to keep the value the same.
1
10^1

17. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
cube-root key
0
10^2

18. The square root of zero is
change both terms in order to keep the value the same.
a fractional decimal
0
Moving the decimal point to the right

19. Negative cube roots are okay ... negative square roots are
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^1
Not
1

20. 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
cube-root key
1
When the exponent of a power-of-10 expression is a negative integer:
10^-2

21. The decimal part
10^-2
perfect square
coefficient
adjust the value of the coefficient

22. Valid powers of 10 for engineering notation are:
5
Same base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
coefficient

23. 0 to any power is equal to
decrease the power-of-10 exponent by the same number of units
0
you have to adjust the value of the exponent in order avoid changing the actual value.
1

24. To find the square root of any number - simply key in the number (the radicand) and press the
Calculator square-root key
Moving the decimal point to the right
base
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

25. The cube root of a negative number is also a
2
10^-18
Are Equal
negative number

26. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
1. Divide the coefficients 2. Subtract the exponents
itself
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

27. The symbol for the cube root of a number is
coefficient
radical sign
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:

28. 1 to any power is equal to
proper scientific
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1
perfect square

29.
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
rewrite one of the terms so that the exponents are equal
exponent
1

30. 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 divided by that number with a positive exponent
increase the power-of-10 exponent by the same number of units
When moving the decimal point to the left (dividing by 10)
perfect square

31. Powers of ten can be added or subtracted only when their exponents
Are Equal
change both terms in order to keep the value the same.
1
Calculator square-root key

32. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
radical sign
increase the power-of-10 exponent by the same number of units
proper scientific

33. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
perfect square
a fractional decimal
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

34. 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
change both terms in order to keep the value the same.
itself
1
perfect square

35. Dividing by 10
Engineering notation
Moving the decimal point to the left
Same base
squared

36. A number is a second number which - when multiplied by itself three times - equals the original number.
5
Scientific notation
cubed
cube root

37. The cube root of zero is
0
10^2
cube-root key
1

38. To multiply or divide exponent terms that do not have the same base:
0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Because 4 multiplied by itself equals 16.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

39. When you move the decimal point in the coefficient to the left
1
2 x 10^9
increase the power-of-10 exponent by the same number of units
base

40. Scientific notation requires there to be only
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
one digit to the left of the decimal point
1. Multiply the coefficients 2. Add the exponents
10^1

41. A number with an exponent of 3 is often said to be
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
cubed
adjust the value of the coefficient
Subtract the exponent

42. 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.
base
3
1 divided by that number with a positive exponent
Engineering notation

43. To add or subtract numbers written with exponents:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
base
The solution exists - but not in the real number system.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

44. 1 to any power is equal to
6.74 x 10^-7
1
Same base
itself

45. For the 10
one digit to the left of the decimal point
exponent
adjust the value of the coefficient
a fractional decimal

46. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
move the decimal point the same number of units to the right
1
10^-18

47. The square of 3 is
9 (3^2 = 9)
proper scientific
squared
decrease the power-of-10 exponent by the same number of units

48. 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.
Because 4 multiplied by itself equals 16.
When the exponent of a power-of-10 expression is a negative integer:
decrease the power-of-10 exponent by the same number of units
Not

49. Numbers with exponents can be directly multiplied or divided only when they have the
Same base
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
3
perfect square

50. 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
9 (3^2 = 9)
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
same exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten