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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. A number is a second number which - when multiplied by itself three times - equals the original number.
0
proper scientific
cube root
one digit to the left of the decimal point

2. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
decrease the power-of-10 exponent by the same number of units
When moving the decimal point to the left (dividing by 10)
Step 1. Divide the coefficients of the terms

3. Multiplying by 10
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
Moving the decimal point to the right
1
10^-1

4. Negative cube roots are okay ... negative square roots are
Not
Are Equal
exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

5.
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
Not
squared
move the decimal point the same number of units to the right

6. When you change the position of the decimal point in a coefficient value
same 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
you have to adjust the value of the exponent in order avoid changing the actual value.
The solution exists - but not in the real number system.

7. 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
decrease the value of the exponent by 1 (dividing by 10)
0
same exponent
cube-root key

8. 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
same exponent
one digit to the left of the decimal point
1. Divide the coefficients 2. Subtract the exponents
decrease the power-of-10 exponent by the same number of units

9. Valid powers-of-10 for engineering notation
same exponent
0
When the exponent of a power-of-10 expression is a negative integer:
must be multiples of 3 or 0

10. 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
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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
5

11. 0^5 =
0
perfect square
Engineering notation
proper scientific

12. To find the square root of any number - simply key in the number (the radicand) and press the
Moving the decimal point to the left
Calculator square-root key
10^-2
The solution exists - but not in the real number system.

13. To divide powers that have the same base:
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
increase the power-of-10 exponent by the same number of units
6.74 x 10^-7

14. Always 10 for scientific notation
base
change both terms in order to keep the value the same.
The solution exists - but not in the real number system.
cube root

15. When you move the decimal point in the coefficient to the right
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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.
a fractional decimal
decrease the power-of-10 exponent by the same number of units

16. When moving the decimal point to the right (multiplying by 10)
Subtract the exponent
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
decrease the value of the exponent by 1 (dividing by 10)

17. The square root of zero is
base
0
5
1

18. Numbers with exponents can be directly multiplied or divided only when they have the
1
0
10^2
Same base

19. To subtract powers of ten:
move the decimal point the same number of units 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
9 (3^2 = 9)
one digit to the left of the decimal point

20. The cube root of zero is
the radical sign with a little 3 that indicates the cube root:
increase the power-of-10 exponent by the same number of units
2
0

21. = 0.01 - or 1 with the decimal point moved two places 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
To multiply powers that 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
10^-2

22. The square of 3 is
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Engineering notation
change both terms in order to keep the value the same.
9 (3^2 = 9)

23. To add or subtract numbers written with exponents:
0
Moving the decimal point to the left
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
10^-2

24. 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.
Scientific notation
Same base
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.

25. Dividing by 10
proper scientific
10^2
10^-2
Moving the decimal point to the left

26. Any number with an exponent of 1 is equal to
change both terms in order to keep the value the same.
Subtract the exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
itself

27. The cube root of a negative number is also a
Because 4 multiplied by itself equals 16.
1
negative number
Same base

28. 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.
proper scientific
Engineering notation
decrease the power-of-10 exponent by the same number of units
6.74 x 10^-7

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
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
move the decimal point the same number of units to the right
exponent
change both terms in order to keep the value the same.

30. A number - when multiplied by itself - is equal to a given number.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
2 x 10^9
square root
0

31. The square root of 9 is
3
must be multiples of 3 or 0
0
10^1

32. Valid powers of 10 for engineering notation are:
coefficient
exponent
Engineering notation
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

33. 10 - or 1 with the decimal point moved one place to the right
increase the power-of-10 exponent by the same number of units
Moving the decimal point to the right
0
10^1

34. A number with an exponent of 2 is often said to be
Calculator square-root key
squared
Because 4 multiplied by itself equals 16.
10^1

35. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
rewrite one of the terms so that the exponents are equal
proper scientific
adjust the value of the coefficient
1

36. 1 to any power is equal to
0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1
change both terms in order to keep the value the same.

37. 1 to any power is equal to
To multiply powers that have the same base:
1
10^1
9 (3^2 = 9)

38. To multiply or divide exponent terms that do not have the same base:
Step 1. Evaluate each term 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
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
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
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
Subtract the exponent

40. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
Scientific notation
1
exponent

41. There are no special rules for adding and subtracting numbers that are written with exponents.
Are Equal
cubed
Same base
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

42. To divide powers of ten:
Engineering notation
1
1. Divide the coefficients 2. Subtract the exponents
0

43. = 0.1 - or 1 with the decimal point moved one place to the left.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
rewrite one of the terms so that the exponents are equal
Because 4 multiplied by itself equals 16.
10^-1

44. Powers of ten can be added or subtracted only when their exponents
Scientific notation
Are Equal
1. Multiply the coefficients 2. Add the exponents
coefficient

45. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
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
exponent

46. 5^1 =
a fractional decimal
squared
5
1. Multiply the coefficients 2. Add the exponents

47. 1^4 =
one digit to the left of the decimal point
When moving the decimal point to the left (dividing by 10)
1
move the decimal point the same number of units to the right

48. To multiply powers of ten:
10^1
exponent
cube root
1. Multiply the coefficients 2. Add the exponents

49. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
1
When the exponent of a power-of-10 expression is a negative integer:
5

50. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
change both terms in order to keep the value the same.
9 (3^2 = 9)
0