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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. 3^0 =
2 x 10^9
exponent
0
1

2. A number - when multiplied by itself - is equal to a given number.
square root
Same base
Not
proper scientific

3. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
1 divided by that number with a positive exponent
0
cube root

4. Represents 1 preceded by 17 zeros and a decimal point.
10^-1
1. Divide the coefficients 2. Subtract the exponents
10^-18
base

5. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
1
squared
exponent

6. 10 - or 1 with the decimal point moved one place to the right
9 (3^2 = 9)
Step 1. Divide the coefficients of the terms
0
10^1

7. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
10^1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
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
Subtract the exponent

8. The square root of 9 is
base
3
2
Calculator square-root key

9. For the 10
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
0
move the decimal point the same number of units to the right
exponent

10. The symbol for the square root of a number is the - a sign placed in front of an expression to denote that a root is to be extracted.
Calculator square-root key
radical sign
1
one digit to the left of the decimal point

11. To add or subtract numbers written with exponents:
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.
decrease the power-of-10 exponent by the same number of units
Same base

12. 1 to any power is equal to
0
Moving the decimal point to the left
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

13. To multiply powers of 10:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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.
base

14. Scientific notation requires there to be only
Because 4 multiplied by itself equals 16.
squared
one digit to the left of the decimal point
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

15. 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.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1
Not

16. Multiplying by 10
Calculator square-root key
10^1
Moving the decimal point to the right
0

17. When moving the decimal point to the right (multiplying by 10)
squared
To multiply powers that have the same base:
decrease the value of the exponent by 1 (dividing by 10)
exponent

18. To divide powers of ten:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1. Divide the coefficients 2. Subtract the exponents
radical sign
move the decimal point the same number of units to the left

19. 100 - or 1 with the decimal point moved two places to the right
perfect square
10^2
one digit to the left of the decimal point
exponent

20. A very small number such as 0.000000674 can be written with scientific notation as
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
6.74 x 10^-7
you have to adjust the value of the exponent in order avoid changing the actual value.
Are Equal

21. When you move the decimal point in the coefficient to the right
Moving the decimal point to the right
decrease the power-of-10 exponent by the same number of units
negative number
you have to adjust the value of the exponent in order avoid changing the actual value.

22. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
0
1. Multiply the coefficients 2. Add the exponents
itself

23. The cube root of a negative number is also a
negative number
rewrite one of the terms so that the exponents are equal
one digit to the left of the decimal point
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

24. Indicates the number of times the base is to be multiplied.
exponent
Same base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
0

25. Powers of ten can be added or subtracted only when their exponents
When the exponent of a power-of-10 expression is a negative integer:
Are Equal
one digit to the left of the decimal point
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

26. To add powers of ten:
0
squared
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0

27. Increase the value of the exponent by 1 (multiplying by 10)
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
6.74 x 10^-7
When moving the decimal point to the left (dividing by 10)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

28. Valid powers-of-10 for engineering notation
Same base
coefficient
must be multiples of 3 or 0
adjust the value of the coefficient

29. 1 to any power is equal to
proper scientific
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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

30. 0 to any power is equal to
0
6.74 x 10^-7
itself
change both terms in order to keep the value the same.

31. Always 10 for scientific notation
a fractional decimal
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
base
1

32. 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
2
adjust the value of the coefficient
9 (3^2 = 9)
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

33. 5^1 =
perfect square
same exponent
To multiply powers that have the same base:
5

34. When you decrease the value of the power-of-10 exponent
2 x 10^9
10^-2
move the decimal point the same number of units to the right
decrease the value of the exponent by 1 (dividing by 10)

35. The cube root of zero is
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
0
1. Multiply the coefficients 2. Add the exponents
coefficient

36. A number with an exponent of 3 is often said to be
cubed
6.74 x 10^-7
Calculator square-root key
Step 1. Divide the coefficients of the terms

37. Dividing by 10
1
Moving the decimal point to the left
0
1

38. Any number with an exponent of 0 is equal to
you have to adjust the value of the exponent in order avoid changing the actual value.
Because 4 multiplied by itself equals 16.
1
cubed

39. Don't bother trying to find the square root of a negative number.
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.
10^1
The solution exists - but not in the real number system.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

40. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Engineering notation
1
Because 4 multiplied by itself equals 16.

41. Indicates the number to be multiplied.
1 divided by that number with a positive exponent
base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
perfect square

42. When you change the position of the decimal point in a coefficient value
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
The solution exists - but not in the real number system.
you have to adjust the value of the exponent in order avoid changing the actual value.
exponent

43. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
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
Moving the decimal point to the left

44. A number is a second number which - when multiplied by itself three times - equals the original number.
cube-root key
base
2
cube root

45. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
10^-1
0
1

46. The square root of zero is
adjust the value of the coefficient
rewrite one of the terms so that the exponents are equal
Are Equal
0

47.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
9 (3^2 = 9)
exponent
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

48. The decimal part
10^-1
Not
When the exponent of a power-of-10 expression is a negative integer:
coefficient

49. To find the square root of any number - simply key in the number (the radicand) and press the
Step 1. Rewrite each number 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
Calculator square-root key
Moving the decimal point to the left

50. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Scientific notation
proper scientific
Same base
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base