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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. 0^5 =
perfect square
0
1
Same base

2. 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.
Scientific notation
1. Multiply the coefficients 2. Add the exponents
Engineering notation
base

3. To multiply powers of 10:
exponent
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. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
9 (3^2 = 9)

4. Scientific notation requires there to be only
one digit to the left of the decimal point
Because 4 multiplied by itself equals 16.
Same base
radical sign

5. Valid powers-of-10 for engineering notation
cube-root key
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
must be multiples of 3 or 0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

6. Indicates the number of times the base is to be multiplied.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Engineering notation
The solution exists - but not in the real number system.
exponent

7. 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
decrease the power-of-10 exponent by the same number of units
base
When the exponent of a power-of-10 expression is a negative integer:

8. Any number with a negative exponent is equal to
0
1 divided by that number with a positive exponent
same exponent
Engineering notation

9. 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.
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. Divide the coefficients 2. Subtract the exponents
Not
Scientific notation

10. To multiply or divide exponent terms that do not have the same base:
exponent
a fractional decimal
0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

11. To add or subtract numbers written with exponents:
cubed
base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

12. When you change the position of the decimal point in a coefficient value
you have to adjust the value of the exponent in order avoid changing the actual value.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
negative number
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

13. To subtract powers of ten:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0
exponent
Engineering notation

14. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
1 divided by that number with a positive exponent
itself
When moving the decimal point to the left (dividing by 10)

15. A very small number such as 0.000000674 can be written with scientific notation as
Because 4 multiplied by itself equals 16.
squared
6.74 x 10^-7
5

16. 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.
Moving the decimal point to the right
10^1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
When the exponent of a power-of-10 expression is a negative integer:

17.
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
2 x 10^9
same exponent
one digit to the left of the decimal point

18. A number with an exponent of 3 is often said to be
exponent
When moving the decimal point to the left (dividing by 10)
adjust the value of the coefficient
cubed

19. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
proper scientific
move the decimal point the same number of units to the left
2
Scientific notation

20. 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
radical sign
Subtract the exponent
Calculator square-root key
same exponent

21. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
Step 1. Divide the coefficients of the terms
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

22. 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.
cube-root key
move the decimal point the same number of units to the right
decrease the value of the exponent by 1 (dividing by 10)
radical sign

23. The cube root of zero is
Subtract the exponent
must be multiples of 3 or 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

24. What number multiplied by itself is equal to 16? The answer is 4. Why?
5
Because 4 multiplied by itself equals 16.
0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

25. 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 divided by that number with a positive exponent
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
0
6.74 x 10^-7

26. When you move the decimal point in the coefficient to the right
change both terms in order to keep the value the same.
0
decrease the power-of-10 exponent by the same number of units
To multiply powers that have the same base:

27. Any number with an exponent of 0 is equal to
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1
When the exponent of a power-of-10 expression is a negative integer:
3

28. Multiplying by 10
one digit to the left of the decimal point
Moving the decimal point to the right
0
base

29. 1 to any power is equal to
itself
move the decimal point the same number of units to the left
exponent
1

30. 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
6.74 x 10^-7
increase the power-of-10 exponent by the same number of units
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

31. To multiply powers of ten:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1. Multiply the coefficients 2. Add the exponents
Engineering notation
0

32. 0 to any power is equal to
square root
0
one digit to the left of the decimal point
1. Divide the coefficients 2. Subtract the exponents

33. The square root of 9 is
1
Same base
3
perfect square

34. A negative exponent does not mean the decimal value is negative. It means the decimal value is
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
a fractional decimal
10^-18
When the exponent of a power-of-10 expression is a negative integer:

35. Dividing by 10
10^-2
adjust the value of the coefficient
Subtract the exponent
Moving the decimal point to the left

36. The square of 3 is
exponent
10^-1
9 (3^2 = 9)
1

37. 1 to any power is equal to
Moving the decimal point to the right
increase the power-of-10 exponent by the same number of units
0
1

38. Don't bother trying to find the square root of a negative number.
The solution exists - but not in the real number system.
squared
0
1. Multiply the coefficients 2. Add the exponents

39. The cube root of a negative number is also a
1
negative number
change both terms in order to keep the value the same.
Step 1. Divide the coefficients of the terms

40. Increase the value of the exponent by 1 (multiplying by 10)
1
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.
When moving the decimal point to the left (dividing by 10)

41. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
2 x 10^9
0
one digit to the left of the decimal point

42. Powers of ten can be added or subtracted only when their exponents
Are Equal
exponent
0
adjust the value of the coefficient

43. 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.
Engineering notation
exponent
0

44. Negative cube roots are okay ... negative square roots are
Are Equal
one digit to the left of the decimal point
Not
Engineering notation

45. When you move the decimal point in the coefficient to the left
base
increase the power-of-10 exponent by the same number of units
change both terms in order to keep the value the same.
must be multiples of 3 or 0

46. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
cube root
Engineering notation
proper scientific

47. A number - when multiplied by itself - is equal to a given number.
1 divided by that number with a positive exponent
Moving the decimal point to the right
square root
the radical sign with a little 3 that indicates the cube root:

48. 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
adjust the value of the coefficient
radical sign
Moving the decimal point to the right
exponent

49. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
must be multiples of 3 or 0
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

50. 5^1 =
When moving the decimal point to the left (dividing by 10)
10^-2
5
itself