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CLEP General Mathematics: Powers Exponents And Roots

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Any number with an exponent of 1 is equal to
decrease the value of the exponent by 1 (dividing by 10)
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
base
itself

2. When you move the decimal point in the coefficient to the right
Calculator square-root key
Engineering notation
square root
decrease the power-of-10 exponent by the same number of units

3. 0^5 =
1
0
you have to adjust the value of the exponent in order avoid changing the actual value.
Step 1. Divide the coefficients of the terms

4. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Scientific notation
0
base
proper scientific

5. = 0.01 - or 1 with the decimal point moved two places to the left.
9 (3^2 = 9)
10^-2
1
The solution exists - but not in the real number system.

6.
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
proper scientific
Calculator square-root key
0

7. For the 10
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
The solution exists - but not in the real number system.
exponent

8. 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.
10^1
Step 1. Divide the coefficients of the terms
Engineering notation
you have to adjust the value of the exponent in order avoid changing the actual value.

9. 1 to any power is equal to
radical sign
coefficient
must be multiples of 3 or 0
1

10. Any number with a negative exponent is equal to
itself
proper scientific
1 divided by that number with a positive exponent
10^-2

11. Indicates the number to be multiplied.
1
negative number
base
proper scientific

12. To divide powers of 10:
Calculator square-root key
1
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

13. To multiply powers of 10:
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.
Moving the decimal point to the left
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. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

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
the radical sign with a little 3 that indicates the cube root:
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
The solution exists - but not in the real number system.

15. A number is a second number which - when multiplied by itself three times - equals the original number.
base
exponent
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.
cube root

16. To multiply powers of ten:
Subtract the exponent
10^-18
Moving the decimal point to the right
1. Multiply the coefficients 2. Add the exponents

17. Scientific notation requires there to be only
1. Multiply the coefficients 2. Add the exponents
Moving the decimal point to the left
one digit to the left of the decimal point
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

18. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
square root
10^-1
change both terms in order to keep the value the same.

19. 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
cube-root key
10^2

20. Any number with an exponent of 0 is equal to
1
cube root
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
the radical sign with a little 3 that indicates the cube root:

21. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
exponent
2 x 10^9
Because 4 multiplied by itself equals 16.
2

22. There are no special rules for adding and subtracting numbers that are written with exponents.
proper scientific
cube-root key
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
move the decimal point the same number of units to the left

23. Valid powers-of-10 for engineering notation
10^2
must be multiples of 3 or 0
one digit to the left of the decimal point
Scientific notation

24. Powers of ten can be added or subtracted only when their exponents
10^-1
you have to adjust the value of the exponent in order avoid changing the actual value.
The solution exists - but not in the real number system.
Are Equal

25. Multiplying by 10
the radical sign with a little 3 that indicates the cube root:
Because 4 multiplied by itself equals 16.
Moving the decimal point to the right
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

26. 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.
Subtract the exponent
same exponent
must be multiples of 3 or 0

27. 1 to any power is equal to
9 (3^2 = 9)
0
1
move the decimal point the same number of units to the left

28. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
5
0
Subtract the exponent
exponent

29. The cube root of zero is
the radical sign with a little 3 that indicates the cube root:
5
0
1

30. Numbers with exponents can be directly multiplied or divided only when they have the
10^-18
When moving the decimal point to the left (dividing by 10)
Step 1. Divide the coefficients of the terms
Same base

31. To add or subtract numbers written with exponents:
Not
you have to adjust the value of the exponent in order avoid changing the actual value.
increase the power-of-10 exponent by the same number of units
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

32. What number multiplied by itself is equal to 16? The answer is 4. Why?
10^-2
Because 4 multiplied by itself equals 16.
you have to adjust the value of the exponent in order avoid changing the actual value.
radical sign

33. 1^4 =
When moving the decimal point to the left (dividing by 10)
1
squared
1 divided by that number with a positive exponent

34. Dividing by 10
proper scientific
Moving the decimal point to the left
Moving the decimal point to the right
exponent

35. 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
cube-root key
10^2
Subtract the exponent

36. 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.
square root
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:
increase the power-of-10 exponent by the same number of units

37. The square of 3 is
exponent
9 (3^2 = 9)
0
Engineering notation

38. The square root of zero is
itself
Moving the decimal point to the left
0
the radical sign with a little 3 that indicates the cube root:

39. 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
base
move the decimal point the same number of units to the left
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

40. To divide powers of ten:
Moving the decimal point to the right
Moving the decimal point to the left
1. Divide the coefficients 2. Subtract the exponents
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

41. 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.
Scientific notation
you have to adjust the value of the exponent in order avoid changing the actual value.
perfect square
base

42. The square root of 9 is
3
10^-18
base
Scientific notation

43. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
0
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.

44. Don't bother trying to find the square root of a negative number.
The solution exists - but not in the real number system.
cube root
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1

45. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
squared
2 x 10^9
move the decimal point the same number of units to the right

46. A number with an exponent of 2 is often said to be
10^2
Moving the decimal point to the left
squared
9 (3^2 = 9)

47. Negative cube roots are okay ... negative square roots are
a fractional decimal
0
1
Not

48. 5^1 =
To multiply powers that have the same base:
5
increase the power-of-10 exponent by the same number of units
square root

49. When you decrease the value of the power-of-10 exponent
rewrite one of the terms so that the exponents are equal
move the decimal point the same number of units to the right
square root
radical sign

50. 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.
negative number
adjust the value of the coefficient
10^2
Scientific notation