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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. There are no special rules for adding and subtracting numbers that are written with exponents.
Step 1. Divide the coefficients of the terms
10^-1
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.

2. The cube root of zero is
10^-2
cube-root key
0
decrease the power-of-10 exponent by the same number of units

3. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Moving the decimal point to the right
2 x 10^9
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
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.

4. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
cube-root key
perfect square
Scientific notation

5. A very small number such as 0.000000674 can be written with scientific notation as
adjust the value of the coefficient
6.74 x 10^-7
Step 1. Divide the coefficients of the terms
decrease the value of the exponent by 1 (dividing by 10)

6. 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.
one digit to the left of the decimal point
When the exponent of a power-of-10 expression is a negative integer:
exponent
1

7. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
proper scientific
rewrite one of the terms so that the exponents are equal
1 divided by that number with a positive exponent

8. Don't bother trying to find the square root of a negative number.
1
The solution exists - but not in the real number system.
cubed
base

9. The decimal part
coefficient
Step 1. Divide the coefficients of the terms
Scientific notation
proper scientific

10. 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
10^-18
Engineering notation

11. 0^5 =
5
0
decrease the value of the exponent by 1 (dividing by 10)
When the exponent of a power-of-10 expression is a negative integer:

12. To add powers of ten:
9 (3^2 = 9)
Scientific notation
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0

13. A number with an exponent of 3 is often said to be
cubed
decrease the value of the exponent by 1 (dividing by 10)
1. Divide the coefficients 2. Subtract the exponents
cube-root key

14. To multiply powers of 10:
Scientific notation
square root
10^-2
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.

15. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
3
squared
proper scientific
1

16. When you move the decimal point in the coefficient to the left
Same base
2 x 10^9
To multiply powers that have the same base:
increase the power-of-10 exponent by the same number of units

17. Negative cube roots are okay ... negative square roots are
must be multiples of 3 or 0
Not
base
10^-2

18. 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
move the decimal point the same number of units to the right
radical sign
Step 1. Divide the coefficients of the terms
same exponent

19. Represents 1 preceded by 17 zeros and a decimal point.
Moving the decimal point to the left
10^-18
base
same exponent

20. To find the square root of any number - simply key in the number (the radicand) and press the
change both terms in order to keep the value the same.
Calculator square-root key
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

21. To divide powers of 10:
cube root
Step 1. Divide the coefficients of the terms
exponent
2 x 10^9

22. 3^0 =
1
Engineering notation
Calculator square-root key
3

23. To divide powers of ten:
negative number
When the exponent of a power-of-10 expression is a negative integer:
Scientific notation
1. Divide the coefficients 2. Subtract the exponents

24. Always 10 for scientific notation
base
Engineering notation
same exponent
1

25.
perfect square
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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:

26. Indicates the number of times the base is to be multiplied.
exponent
one digit to the left of the 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
negative number

27. 100 - or 1 with the decimal point moved two places to the right
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^2
decrease the value of the exponent by 1 (dividing by 10)

28. Indicates the number to be multiplied.
exponent
base
proper scientific
cubed

29. Scientific notation requires there to be only
proper scientific
1
move the decimal point the same number of units to the left
one digit to the left of the decimal point

30. Dividing by 10
Moving the decimal point to the left
proper scientific
a fractional decimal
1

31. When you increase the value of the power-of-10 exponent
Engineering notation
move the decimal point the same number of units to the left
decrease the power-of-10 exponent by the same number of units
5

32. For the 10
coefficient
5
0
exponent

33. 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
0
adjust the value of the coefficient
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Not

34. 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
adjust the value of the coefficient
increase the power-of-10 exponent by the same number of units
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
square root

35. The cube root of a negative number is also a
negative number
10^1
the radical sign with a little 3 that indicates the cube root:
itself

36. 1 to any power is equal to
exponent
Calculator square-root key
change both terms in order to keep the value the same.
1

37. 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
cube-root key
exponent
negative number
adjust the value of the coefficient

38. 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
base
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.
the radical sign with a little 3 that indicates the cube root:

39. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
perfect square
cubed
exponent

40. A negative exponent does not mean the decimal value is negative. It means the decimal value is
proper scientific
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
base

41. To add or subtract numbers written with exponents:
0
Moving the decimal point to the right
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
decrease the value of the exponent by 1 (dividing by 10)

42. To multiply or divide exponent terms that do not have the same base:
1
a fractional decimal
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
2 x 10^9

43. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
When moving the decimal point to the left (dividing by 10)
1. Divide the coefficients 2. Subtract the exponents
Step 1. Divide the coefficients of the terms

44. 0 to any power is equal to
0
1. Multiply the coefficients 2. Add the exponents
perfect square
proper scientific

45. The square root of zero is
0
move the decimal point the same number of units to the right
Are Equal
Subtract the exponent

46. 1^4 =
perfect square
coefficient
1
rewrite one of the terms so that the exponents are equal

47. A number with an exponent of 2 is often said to be
Engineering notation
squared
2 x 10^9
0

48. When you change the position of the decimal point in a coefficient value
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
you have to adjust the value of the exponent in order avoid changing the actual value.
0
increase the power-of-10 exponent by the same number of units

49. Any number with an exponent of 1 is equal to
move the decimal point the same number of units to the right
itself
6.74 x 10^-7
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

50. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
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
change both terms in order to keep the value the same.
1