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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 number with an exponent of 3 is often said to be
proper scientific
10^-2
cubed
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

2. Step 1: Add the exponents Step 2: Use the common base
10^-18
To multiply powers that have the same base:
base
Moving the decimal point to the right

3. Negative cube roots are okay ... negative square roots are
2 x 10^9
Not
0
the radical sign with a little 3 that indicates the cube root:

4. To divide powers of ten:
must be multiples of 3 or 0
1. Divide the coefficients 2. Subtract the exponents
squared
10^-18

5. When you move the decimal point in the coefficient to the left
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
increase the power-of-10 exponent by the same number of units
adjust the value of the coefficient

6. The symbol for the cube root of a number is
exponent
1
the radical sign with a little 3 that indicates the cube root:
1. Divide the coefficients 2. Subtract the exponents

7. Numbers with exponents can be directly multiplied or divided only when they have the
coefficient
1 divided by that number with a positive exponent
1
Same base

8. Multiplying by 10
10^-1
Scientific notation
1
Moving the decimal point to the right

9. 1^4 =
coefficient
2
1
adjust the value of the coefficient

10. To multiply powers of 10:
perfect square
1
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.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

11. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
exponent
Scientific notation
coefficient

12. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
decrease the value of the exponent by 1 (dividing by 10)
Engineering notation
2
1

13. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
cubed
10^1
2 x 10^9

14. = 0.1 - or 1 with the decimal point moved one place to the left.
base
Not
10^-1
itself

15. Any number with an exponent of 0 is equal to
increase the power-of-10 exponent by the same number of units
1
1. Divide the coefficients 2. Subtract the exponents
Step 1. Divide the coefficients of the terms

16. A number with an exponent of 2 is often said to be
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1 divided by that number with a positive exponent
squared
Because 4 multiplied by itself equals 16.

17. What number multiplied by itself is equal to 16? The answer is 4. Why?
radical sign
Because 4 multiplied by itself equals 16.
1 divided by that number with a positive exponent
0

18. The decimal part
base
coefficient
The solution exists - but not in the real number system.
move the decimal point the same number of units to the left

19. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
move the decimal point the same number of units to the left
0
0

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.
exponent
cubed
proper scientific
When the exponent of a power-of-10 expression is a negative integer:

21. Indicates the number of times the base is to be multiplied.
1. Multiply the coefficients 2. Add the exponents
exponent
proper scientific
rewrite one of the terms so that the exponents are equal

22. Powers of ten can be added or subtracted only when their exponents
a fractional decimal
Moving the decimal point to the left
Are Equal
0

23. 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
same exponent
radical sign
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Moving the decimal point to the left

24. Scientific notation requires there to be only
10^-2
one digit to the left of the decimal point
itself
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

25. Don't bother trying to find the square root of a negative number.
cube-root key
1. Multiply the coefficients 2. Add the exponents
2 x 10^9
The solution exists - but not in the real number system.

26. 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.
radical sign
itself
1
proper scientific

27. Indicates the number to be multiplied.
cube-root key
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
base
decrease the power-of-10 exponent by the same number of units

28. A very small number such as 0.000000674 can be written with scientific notation as
Not
Scientific notation
6.74 x 10^-7
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

29. To add or subtract numbers written with exponents:
must be multiples of 3 or 0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

30. To divide powers of 10:
9 (3^2 = 9)
Step 1. Divide the coefficients of the terms
coefficient
1

31. 0 to any power is equal to
decrease the power-of-10 exponent by the same number of units
Subtract the exponent
Scientific notation
0

32. 0^5 =
10^1
0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^2

33. When you change the position of the decimal point in a coefficient value
Calculator square-root key
one digit to the left of the decimal point
0
you have to adjust the value of the exponent in order avoid changing the actual value.

34. The square root of 9 is
must be multiples of 3 or 0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
2
3

35. 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
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
decrease the power-of-10 exponent by the same number of units
0

36. When you increase the value of the power-of-10 exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
proper scientific
10^1
move the decimal point the same number of units to the left

37. To add powers of ten:
2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Not
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

38. 1 to any power is equal to
1
Calculator square-root key
Are Equal
square root

39. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
must be multiples of 3 or 0
0
perfect square
Subtract the exponent

40. To subtract powers of ten:
rewrite one of the terms so that the exponents are equal
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0
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

41. Represents 1 preceded by 17 zeros and a decimal point.
0
Moving the decimal point to the left
10^-18
the radical sign with a little 3 that indicates the cube root:

42. The square root of zero is
0
increase the power-of-10 exponent by the same number of units
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Not

43. 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.
To multiply powers that have the same base:
Scientific notation
Not
Are Equal

44. Valid powers of 10 for engineering notation are:
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Same base
Moving the decimal point to the left

45. 10 - or 1 with the decimal point moved one place to the right
itself
coefficient
10^1
decrease the value of the exponent by 1 (dividing by 10)

46. 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
10^2
change both terms in order to keep the value the same.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Step 1. Divide the coefficients of the terms

47. A number - when multiplied by itself - is equal to a given number.
square root
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^1

48. The cube root of a negative number is also a
10^-2
the radical sign with a little 3 that indicates the cube root:
negative number
cubed

49. When you move the decimal point in the coefficient to the right
6.74 x 10^-7
decrease the power-of-10 exponent by the same number of units
Are Equal
Subtract the exponent

50. To multiply or divide exponent terms that do not have the same base:
When moving the decimal point to the left (dividing by 10)
negative number
change both terms in order to keep the value the same.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.