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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 subtract powers of ten:
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
cube root
Are Equal

2. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
squared
10^1
2
base

3. Indicates the number to be multiplied.
negative number
base
1. Divide the coefficients 2. Subtract the exponents
1

4. Don't bother trying to find the square root of a negative number.
10^-18
0
Engineering notation
The solution exists - but not in the real number system.

5. 5^1 =
5
2
proper scientific
1

6. To multiply powers of ten:
1
proper scientific
1. Multiply the coefficients 2. Add the exponents
Not

7. A number with an exponent of 2 is often said to be
coefficient
squared
2
rewrite one of the terms so that the exponents are equal

8. 0^5 =
1 divided by that number with a positive exponent
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

9. A number - when multiplied by itself - is equal to a given number.
10^-18
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1
square root

10. Step 1: Add the exponents Step 2: Use the common base
proper scientific
To multiply powers that have the same base:
1
2

11. Valid powers of 10 for engineering notation are:
you have to adjust the value of the exponent in order avoid changing the actual value.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1. Multiply the coefficients 2. Add the exponents
decrease the power-of-10 exponent by the same number of units

12. Any number with a negative exponent is equal to
move the decimal point the same number of units to the right
1 divided by that number with a positive exponent
exponent
Engineering notation

13. 10 - or 1 with the decimal point moved one place to the right
10^1
perfect square
move the decimal point the same number of units to the right
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

14. 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
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
2 x 10^9
0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

15. The square root of 9 is
0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
3
base

16. When you decrease the value of the power-of-10 exponent
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
move the decimal point the same number of units to the right

17. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
5
Moving the decimal point to the left
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

18. 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.
10^1
Scientific notation
5
one digit to the left of the decimal point

19. 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.
change both terms in order to keep the value the same.
decrease the value of the exponent by 1 (dividing by 10)
0

20. To add or subtract numbers written with exponents:
Same base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
increase the power-of-10 exponent by the same number of units
same exponent

21. 100 - or 1 with the decimal point moved two places to the right
you have to adjust the value of the exponent in order avoid changing the actual value.
10^-18
10^2
base

22. When moving the decimal point to the right (multiplying by 10)
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1
the radical sign with a little 3 that indicates the cube root:
decrease the value of the exponent by 1 (dividing by 10)

23.
Are Equal
When moving the decimal point to the left (dividing by 10)
10^2
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

24. = 0.01 - or 1 with the decimal point moved two places to the left.
increase the power-of-10 exponent by the same number of units
base
10^-2
Calculator square-root key

25. When you move the decimal point in the coefficient to the left
10^2
increase the power-of-10 exponent by the same number of units
proper scientific
Moving the decimal point to the left

26. To divide powers of 10:
10^2
Step 1. Divide the coefficients of the terms
exponent
1

27. 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
1
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
cube-root key

28. The cube root of zero is
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
0
1
cubed

29. Powers of ten can be added or subtracted only when their exponents
Are Equal
10^-2
9 (3^2 = 9)
5

30. Valid powers-of-10 for engineering notation
Engineering notation
must be multiples of 3 or 0
3
perfect square

31. The decimal part
adjust the value of the coefficient
To multiply powers that have the same base:
proper scientific
coefficient

32. 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
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
base
same exponent
Because 4 multiplied by itself equals 16.

33. Scientific notation requires there to be only
10^-1
proper scientific
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

34. To add 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
0
cube root
2

35. Represents 1 preceded by 17 zeros and a decimal point.
base
10^-18
square root
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

36. When you increase the value of the power-of-10 exponent
To multiply powers that have the same base:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
a fractional decimal
move the decimal point the same number of units to the left

37. 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.
square root
1
Because 4 multiplied by itself equals 16.

38. Numbers with exponents can be directly multiplied or divided only when they have the
1 divided by that number with a positive exponent
squared
Same base
2 x 10^9

39. To multiply or divide exponent terms that do not have the same base:
1. Multiply the coefficients 2. Add the exponents
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
a fractional decimal
coefficient

40. Any number with an exponent of 1 is equal to
1 divided by that number with a positive exponent
itself
Engineering notation
you have to adjust the value of the exponent in order avoid changing the actual value.

41. 1^4 =
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
When the exponent of a power-of-10 expression is a negative integer:
base
1

42. There are no special rules for adding and subtracting numbers that are written with exponents.
0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
0
radical sign

43. 1 to any power is equal to
cubed
one digit to the left of the decimal point
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1

44. 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 left
When the exponent of a power-of-10 expression is a negative integer:
10^2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

45. To divide powers of ten:
square root
1. Divide the coefficients 2. Subtract the exponents
0
cubed

46. The square root of zero is
radical sign
Step 1. Divide the coefficients of the terms
1
0

47. To divide powers that have the same base:
Same base
1 divided by that number with a positive exponent
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.

48. A number with an exponent of 3 is often said to be
cubed
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
0
10^1

49. A negative exponent does not mean the decimal value is negative. It means the decimal value is
cube root
a fractional decimal
radical sign
Same base

50. A very small number such as 0.000000674 can be written with scientific notation as
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
6.74 x 10^-7
the radical sign with a little 3 that indicates the cube root:
2