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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. 1 to any power is equal to
1
move the decimal point the same number of units to the left
itself
0

2. = 0.01 - or 1 with the decimal point moved two places to the left.
Engineering notation
10^-2
rewrite one of the terms so that the exponents are equal
1

3. When moving the decimal point to the right (multiplying by 10)
1. Multiply the coefficients 2. Add the exponents
Subtract the exponent
base
decrease the value of the exponent by 1 (dividing by 10)

4. A number - when multiplied by itself - is equal to a given number.
1
square root
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.
To multiply powers that have the same base:

5. To multiply or divide exponent terms that do not have the same base:
proper scientific
Moving the decimal point to the right
Because 4 multiplied by itself equals 16.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

6. To divide powers that have the same base:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^1
3

7. The decimal part
coefficient
When moving the decimal point to the left (dividing by 10)
Subtract the exponent
must be multiples of 3 or 0

8. 0^5 =
0
Same base
1
1. Divide the coefficients 2. Subtract the exponents

9. 0 to any power is equal to
Are Equal
Moving the decimal point to the right
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

10. A number with an exponent of 2 is often said to be
adjust the value of the coefficient
10^1
cube-root key
squared

11. Dividing by 10
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Moving the decimal point to the left
you have to adjust the value of the exponent in order avoid changing the actual value.
10^2

12. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
one digit to the left of the decimal point
proper scientific
10^2
1

13. When the exponents are not the same
adjust the value of the coefficient
rewrite one of the terms so that the exponents are equal
1
you have to adjust the value of the exponent in order avoid changing the actual value.

14. 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.
2 x 10^9
Engineering notation
coefficient
squared

15. Valid powers-of-10 for engineering notation
The solution exists - but not in the real number system.
move the decimal point the same number of units to the right
must be multiples of 3 or 0
1 divided by that number with a positive exponent

16. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
cubed
0

17. To subtract powers of ten:
itself
2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
increase the power-of-10 exponent by the same number of units

18. 3^0 =
Same base
1
you have to adjust the value of the exponent in order avoid changing the actual value.
negative number

19. 1 to any power is equal to
coefficient
1
rewrite one of the terms so that the exponents are equal
decrease the value of the exponent by 1 (dividing by 10)

20. To add or subtract numbers written with exponents:
1
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
Calculator square-root key
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

21. The symbol for the cube root of a number is
negative number
the radical sign with a little 3 that indicates the cube root:
When moving the decimal point to the left (dividing by 10)
1

22. 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
6.74 x 10^-7
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 left

23. There are no special rules for adding and subtracting numbers that are written with exponents.
1 divided by that number with a positive exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^-2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

24. To add powers of ten:
same exponent
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
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

25. 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.
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
Same base
1
When the exponent of a power-of-10 expression is a negative integer:

26. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Engineering notation
1
a fractional decimal
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

27. The square root of 9 is
10^2
3
1
the radical sign with a little 3 that indicates the cube root:

28. Valid powers of 10 for engineering notation are:
cube root
To multiply powers that have the same base:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
squared

29. 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.
base
0
Subtract the exponent

30. Always 10 for scientific notation
cube-root key
To multiply powers that have the same base:
base
Subtract the exponent

31. 1^4 =
Step 1. Divide the coefficients of the terms
move the decimal point the same number of units to the right
base
1

32. 100 - or 1 with the decimal point moved two places to the right
When the exponent of a power-of-10 expression is a negative integer:
10^2
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
adjust the value of the coefficient

33. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
radical sign
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Moving the decimal point to the left

34. = 0.1 - or 1 with the decimal point moved one place to the left.
square root
0
10^-1
To multiply powers that have the same base:

35.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
same exponent
cube root
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

36. The cube root of a negative number is also a
a fractional decimal
negative number
1
Calculator square-root key

37. To divide powers of ten:
Same base
1. Divide the coefficients 2. Subtract the exponents
cubed
1

38. What number multiplied by itself is equal to 16? The answer is 4. Why?
change both terms in order to keep the value the same.
1
Scientific notation
Because 4 multiplied by itself equals 16.

39. To multiply powers of ten:
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. Multiply the coefficients 2. Add the exponents
1
Engineering notation

40. For the 10
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
3
exponent

41. 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
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Divide the coefficients of the terms
1
change both terms in order to keep the value the same.

42. Don't bother trying to find the square root of a negative number.
proper scientific
one digit to the left of the decimal point
1
The solution exists - but not in the real number system.

43. Any number with a negative exponent 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
10^-18
0
1 divided by that number with a positive exponent

44. When you move the decimal point in the coefficient to the left
a fractional decimal
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
2

45. Scientific notation requires there to be only
5
cubed
one digit to the left of the decimal point
cube root

46. When you decrease the value of the power-of-10 exponent
Same base
decrease the value of the exponent by 1 (dividing by 10)
proper scientific
move the decimal point the same number of units to the right

47. Multiplying by 10
1
10^-1
Moving the decimal point to the right
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

48. To divide powers of 10:
Same base
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Not
Step 1. Divide the coefficients of the terms

49. When you move the decimal point in the coefficient to the right
2
decrease the power-of-10 exponent by the same number of units
1
change both terms in order to keep the value the same.

50. Negative cube roots are okay ... negative square roots are
2 x 10^9
When the exponent of a power-of-10 expression is a negative integer:
one digit to the left of the decimal point
Not