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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. Increase the value of the exponent by 1 (multiplying by 10)
1
When moving the decimal point to the left (dividing by 10)
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
3

2. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
a fractional decimal
Are Equal
0

3. 0^5 =
1
rewrite one of the terms so that the exponents are equal
1. Divide the coefficients 2. Subtract the exponents
0

4. 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.
Because 4 multiplied by itself equals 16.
move the decimal point the same number of units to the left
1. Multiply the coefficients 2. Add the exponents

5. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
0
cube-root key
1. Multiply the coefficients 2. Add the exponents

6. To find the square root of any number - simply key in the number (the radicand) and press the
increase the power-of-10 exponent by the same number of units
0
Calculator square-root key
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

7. To multiply powers of ten:
Subtract the exponent
Moving the decimal point to the left
10^1
1. Multiply the coefficients 2. Add the exponents

8. 1 to any power is equal to
Engineering notation
1
2
adjust the value of the coefficient

9. The symbol for the cube root of a number is
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
change both terms in order to keep the value the same.
the radical sign with a little 3 that indicates the cube root:
5

10. Dividing by 10
cubed
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
Moving the decimal point to the left

11. When you move the decimal point in the coefficient to the left
1. Multiply the coefficients 2. Add the exponents
10^2
increase the power-of-10 exponent by the same number of units
same exponent

12. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
10^1
5
Moving the decimal point to the right

13. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Calculator square-root key
1. Multiply the coefficients 2. Add the exponents
2 x 10^9
Subtract the exponent

14. To add or subtract numbers written with exponents:
base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Not
The solution exists - but not in the real number system.

15. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
cube-root key
Because 4 multiplied by itself equals 16.
radical sign

16. Any number with an exponent of 1 is equal to
1. Divide the coefficients 2. Subtract the exponents
10^-2
9 (3^2 = 9)
itself

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

18. When you change the position of the decimal point in a coefficient value
10^1
Engineering notation
0
you have to adjust the value of the exponent in order avoid changing the actual value.

19. 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
0
same exponent
1
1

20. 1^4 =
negative number
cubed
1
base

21. A very small number such as 0.000000674 can be written with scientific notation as
Moving the decimal point to the left
6.74 x 10^-7
itself
1 divided by that number with a positive exponent

22. Powers of ten can be added or subtracted only when their exponents
proper scientific
Are Equal
Because 4 multiplied by itself equals 16.
1

23. 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
Step 1. Divide the coefficients of the terms
square root
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

24. 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
Engineering notation
0
When the exponent of a power-of-10 expression is a negative integer:

25. 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.
cube-root key
must be multiples of 3 or 0
1

26. Don't bother trying to find the square root of a negative number.
10^1
0
2 x 10^9
The solution exists - but not in the real number system.

27. 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 value of the exponent by 1 (dividing by 10)
base
When the exponent of a power-of-10 expression is a negative integer:

28. Indicates the number to be multiplied.
1. Divide the coefficients 2. Subtract the exponents
base
decrease the value of the exponent by 1 (dividing by 10)
coefficient

29. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
move the decimal point the same number of units to the left
5

30. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
radical sign
cubed
proper scientific
When moving the decimal point to the left (dividing by 10)

31. 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
adjust the value of the coefficient
Not
one digit to the left of the decimal point

32. 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.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
decrease the value of the exponent by 1 (dividing by 10)
adjust the value of the coefficient
When the exponent of a power-of-10 expression is a negative integer:

33. 100 - or 1 with the decimal point moved two places to the right
move the decimal point the same number of units to the left
move the decimal point the same number of units to the right
rewrite one of the terms so that the exponents are equal
10^2

34. 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.
cube-root key
10^-1
Scientific notation
the radical sign with a little 3 that indicates the cube root:

35. To multiply or divide exponent terms that do not have the same base:
Step 1. Divide the coefficients of the terms
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
proper scientific
coefficient

36. Any number with an exponent of 0 is equal to
When moving the decimal point to the left (dividing by 10)
exponent
1
negative number

37. Any number with a negative exponent is equal to
6.74 x 10^-7
one digit to the left of the decimal point
1 divided by that number with a positive exponent
Not

38.
When moving the decimal point to the left (dividing by 10)
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
move the decimal point the same number of units to the left
1. Multiply the coefficients 2. Add the exponents

39. To add powers of ten:
itself
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
3
10^-2

40. 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
perfect square
squared
move the decimal point the same number of units to the left

41. A negative exponent does not mean the decimal value is negative. It means the decimal value is
1
cube root
a fractional decimal
base

42. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
To multiply powers that have the same base:
0
base

43. The decimal part
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1
coefficient
exponent

44. Multiplying by 10
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Moving the decimal point to the right
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
itself

45. 1 to any power is equal to
3
2
one digit to the left of the decimal point
1

46. When moving the decimal point to the right (multiplying by 10)
1
decrease the value of the exponent by 1 (dividing by 10)
change both terms in order to keep the value the same.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

47. 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.
you have to adjust the value of the exponent in order avoid changing the actual value.
cubed
a fractional decimal

48. For the 10
perfect square
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
9 (3^2 = 9)
exponent

49. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
square root
10^-1
perfect square

50. = 0.01 - or 1 with the decimal point moved two places to the left.
itself
10^-2
9 (3^2 = 9)
3