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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. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
0
0
10^-1
2 x 10^9

2. To find the square root of any number - simply key in the number (the radicand) and press the
10^2
squared
The solution exists - but not in the real number system.
Calculator square-root key

3. Numbers with exponents can be directly multiplied or divided only when they have the
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
change both terms in order to keep the value the same.
9 (3^2 = 9)
Same base

4. A number - when multiplied by itself - is equal to a given number.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1 divided by that number with a positive exponent
cube root
square root

5. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
proper scientific
decrease the power-of-10 exponent by the same number of units
9 (3^2 = 9)

6. The decimal part
coefficient
2
cubed
Same base

7. 1^4 =
0
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
you have to adjust the value of the exponent in order avoid changing the actual value.

8. 100 - or 1 with the decimal point moved two places to the right
must be multiples of 3 or 0
10^2
proper scientific
exponent

9. 0^5 =
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
0
Scientific notation
6.74 x 10^-7

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

11. To divide powers of 10:
0
10^-1
Step 1. Divide the coefficients of the terms
rewrite one of the terms so that the exponents are equal

12. A very small number such as 0.000000674 can be written with scientific notation as
Scientific notation
2
6.74 x 10^-7
cube root

13. When you increase the value of the power-of-10 exponent
9 (3^2 = 9)
0
move the decimal point the same number of units to the left
1

14. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
must be multiples of 3 or 0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
5

15. = 0.1 - or 1 with the decimal point moved one place to the left.
one digit to the left of the decimal point
cubed
base
10^-1

16. Any number with an exponent of 0 is equal to
The solution exists - but not in the real number system.
Same base
1
square root

17. Multiplying by 10
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
coefficient
1
Moving the decimal point to the right

18. = 0.01 - or 1 with the decimal point moved two places to the left.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
perfect square
10^-2
0

19. The square of 3 is
9 (3^2 = 9)
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
change both terms in order to keep the value the same.
The solution exists - but not in the real number system.

20. 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. Divide the coefficients of the terms
10^-2
When the exponent of a power-of-10 expression is a negative integer:
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.

21. To add powers of ten:
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
10^-18
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

22. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1. Divide the coefficients 2. Subtract the exponents
10^-18
proper scientific

23. 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.
10^2
Moving the decimal point to the right
The solution exists - but not in the real number system.

24. To multiply powers of ten:
0
2
perfect square
1. Multiply the coefficients 2. Add the exponents

25. The symbol for the cube root of a number is
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.
the radical sign with a little 3 that indicates the cube root:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

26. 0 to any power is equal to
0
1
1. Multiply the coefficients 2. Add the exponents
the radical sign with a little 3 that indicates the cube root:

27. Any number with a negative exponent is equal to
6.74 x 10^-7
you have to adjust the value of the exponent in order avoid changing the actual value.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1 divided by that number with a positive exponent

28. To divide powers of ten:
exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1. Divide the coefficients 2. Subtract the exponents
Engineering notation

29. Increase the value of the exponent by 1 (multiplying by 10)
5
When moving the decimal point to the left (dividing by 10)
10^-2
square root

30. 10 - or 1 with the decimal point moved one place to the right
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^1
cube-root key
To multiply powers that have the same base:

31. 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.
Not
Because 4 multiplied by itself equals 16.
adjust the value of the coefficient

32. Valid powers of 10 for engineering notation are:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1
Engineering notation
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

33. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
base
itself
9 (3^2 = 9)

34. To multiply powers of 10:
10^-2
When the exponent of a power-of-10 expression is a negative integer:
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.
you have to adjust the value of the exponent in order avoid changing the actual value.

35. 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
1
2
adjust the value of the coefficient
1

36. To multiply or divide exponent terms that do not have the same base:
squared
cube root
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
base

37. The square root of 9 is
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Calculator square-root key
3
adjust the value of the coefficient

38. For the 10
itself
decrease the power-of-10 exponent by the same number of units
radical sign
exponent

39. Always 10 for scientific notation
base
To multiply 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
Not

40. Negative cube roots are okay ... negative square roots are
Not
rewrite one of the terms so that the exponents are equal
10^-18
one digit to the left of the decimal point

41. When moving the decimal point to the right (multiplying by 10)
2 x 10^9
base
When the exponent of a power-of-10 expression is a negative integer:
decrease the value of the exponent by 1 (dividing by 10)

42. The cube root of zero is
0
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.
negative number

43.
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
square root
When moving the decimal point to the left (dividing by 10)

44. When the exponents are not the same
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.
rewrite one of the terms so that the exponents are equal
0
Engineering notation

45. 5^1 =
5
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Divide the coefficients of the terms

46. 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.
adjust the value of the coefficient
exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Scientific notation

47. The cube root of a negative number is also a
negative number
Moving the decimal point to the right
Moving the decimal point to the left
0

48. Indicates the number of times the base is to be multiplied.
Moving the decimal point to the right
exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
change both terms in order to keep the value the same.

49. Powers of ten can be added or subtracted only when their exponents
5
1 divided by that number with a positive exponent
Are Equal
1. Multiply the coefficients 2. Add the exponents

50. The square root of zero is
0
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.
move the decimal point the same number of units to the right
1