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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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 divide powers that have the same base:
cube-root key
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Moving the decimal point 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

2. A number with an exponent of 3 is often said to be
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Are Equal
1
cubed

3.
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
1
1

4. Multiplying by 10
0
Scientific notation
rewrite one of the terms so that the exponents are equal
Moving the decimal point to the right

5. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Engineering notation
Moving the decimal point to the left

6. Don't bother trying to find the square root of a negative number.
1. Divide the coefficients 2. Subtract the exponents
increase the power-of-10 exponent by the same number of units
The solution exists - but not in the real number system.
10^-1

7. To divide powers of ten:
base
squared
decrease the value of the exponent by 1 (dividing by 10)
1. Divide the coefficients 2. Subtract the exponents

8. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
rewrite one of the terms so that the exponents are equal
10^-2
To multiply powers that have the same base:

9. 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
When moving the decimal point to the left (dividing 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
cube root
2

10. Scientific notation requires there to be only
one digit to the left of the decimal point
Scientific notation
10^-1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

11. 1 to any power is equal to
10^-18
10^-2
1
increase the power-of-10 exponent by the same number of units

12. Numbers with exponents can be directly multiplied or divided only when they have the
decrease the power-of-10 exponent by the same number of units
Same base
move the decimal point the same number of units to the right
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.

13. The square root of 9 is
3
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

14. To divide powers of 10:
Not
Step 1. Divide the coefficients of the terms
one digit to the left of the decimal point
radical sign

15. 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
2 x 10^9
2
When the exponent of a power-of-10 expression is a negative integer:

16. 1 to any power is equal to
move the decimal point the same number of units to the left
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1
move the decimal point the same number of units to the right

17. Powers of ten can be added or subtracted only when their exponents
Are Equal
exponent
Calculator square-root key
10^-1

18. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
base
The solution exists - but not in the real number system.
Calculator square-root key

19. When you decrease the value of the power-of-10 exponent
1
10^1
move the decimal point the same number of units to the right
1

20. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1
0
2
Scientific notation

21. The cube root of zero is
0
proper scientific
Moving the decimal point to the left
change both terms in order to keep the value the same.

22. To find the square root of any number - simply key in the number (the radicand) and press the
10^1
3
Calculator square-root key
0

23. 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
cubed
rewrite one of the terms so that the exponents are equal

24. = 0.01 - or 1 with the decimal point moved two places to the left.
10^1
Moving the decimal point to the right
10^-2
cube root

25. To multiply powers of ten:
cube root
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
1. Multiply the coefficients 2. Add the exponents

26. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Not
2 x 10^9
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
square root

27. Indicates the number to be multiplied.
rewrite one of the terms so that the exponents are equal
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
base

28. 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
same exponent
cube-root key
When the exponent of a power-of-10 expression is a negative integer:
9 (3^2 = 9)

29. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
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.
1. Divide the coefficients 2. Subtract the exponents

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

31. The decimal part
1
coefficient
you have to adjust the value of the exponent in order avoid changing the actual value.
2 x 10^9

32. 3^0 =
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^2
move the decimal point the same number of units to the left
1

33. When you move the decimal point in the coefficient to the right
decrease the power-of-10 exponent by the same number of units
1. Divide the coefficients 2. Subtract the exponents
The solution exists - but not in the real number system.
When the exponent of a power-of-10 expression is a negative integer:

34. Valid powers of 10 for engineering notation are:
Moving the decimal point to the right
exponent
one digit to the left of the decimal point
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

35. Valid powers-of-10 for engineering notation
exponent
must be multiples of 3 or 0
5
1

36. 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
1
a fractional decimal
9 (3^2 = 9)
same exponent

37. For the 10
exponent
1 divided by that number with a positive exponent
1
decrease the value of the exponent by 1 (dividing by 10)

38. Increase the value of the exponent by 1 (multiplying by 10)
0
must be multiples of 3 or 0
When moving the decimal point to the left (dividing by 10)
10^2

39. Represents 1 preceded by 17 zeros and a decimal point.
0
squared
1. Multiply the coefficients 2. Add the exponents
10^-18

40. The square root of zero is
0
adjust the value of the coefficient
Engineering notation
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

41. When moving the decimal point to the right (multiplying by 10)
2 x 10^9
decrease the value of the exponent by 1 (dividing by 10)
Calculator square-root key
1

42. A number with an exponent of 2 is often said to be
Are Equal
squared
Same base
1

43. 0^5 =
Engineering notation
10^-18
0
proper scientific

44. 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
base
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

45. Dividing by 10
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
move the decimal point the same number of units to the right
Moving the decimal point to the left

46. Any number with a negative exponent is equal to
To multiply powers that have the same base:
10^-2
decrease the value of the exponent by 1 (dividing by 10)
1 divided by that number with a positive exponent

47. Any number with an exponent of 1 is equal to
itself
Moving the decimal point to the right
Moving the decimal point to the left
Because 4 multiplied by itself equals 16.

48. 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.
0
Engineering notation
rewrite one of the terms so that the exponents are equal
1 divided by that number with a positive exponent

49. The symbol for the cube root of a number is
5
coefficient
Because 4 multiplied by itself equals 16.
the radical sign with a little 3 that indicates the cube root:

50. 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
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
exponent
Subtract the exponent