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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. Powers of ten can be added or subtracted only when their exponents
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
When the exponent of a power-of-10 expression is a negative integer:
Are Equal
base

2. = 0.1 - or 1 with the decimal point moved one place to the left.
same exponent
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
cube root
10^-1

3. When you increase the value of the power-of-10 exponent
base
coefficient
2 x 10^9
move the decimal point the same number of units to the left

4. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
Moving the decimal point to the left
0
must be multiples of 3 or 0

5. 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.
0
Scientific notation
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
perfect square

6. 1 to any power is equal to
move the decimal point the same number of units to the right
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
base

7. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
cube-root key
Subtract the exponent
change both terms in order to keep the value the same.

8. 0^5 =
Subtract the exponent
0
coefficient
move the decimal point the same number of units to the right

9. 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.
you have to adjust the value of the exponent in order avoid changing the actual value.
radical sign
When moving the decimal point to the left (dividing by 10)
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

10. = 0.01 - or 1 with the decimal point moved two places to the left.
cube root
The solution exists - but not in the real number system.
10^-2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

11. Any number with a negative exponent is equal to
Moving the decimal point to the right
1 divided by that number with a positive exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-1

12. To multiply or divide exponent terms that do not have the same base:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
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.
proper scientific
0

13. Scientific notation requires there to be only
0
exponent
square root
one digit to the left of the decimal point

14. Multiplying by 10
itself
the radical sign with a little 3 that indicates the cube root:
Scientific notation
Moving the decimal point to the right

15. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
same exponent
Calculator square-root key
Moving the decimal point to the left
2 x 10^9

16. Numbers with exponents can be directly multiplied or divided only when they have the
rewrite one of the terms so that the exponents are equal
Step 1. Divide the coefficients of the terms
same exponent
Same base

17. Any number with an exponent of 1 is equal to
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
exponent
1
itself

18.
Calculator square-root key
decrease the power-of-10 exponent by the same number of units
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
base

19. When you move the decimal point in the coefficient to the right
1
same exponent
proper scientific
decrease the power-of-10 exponent by the same number of units

20. A number with an exponent of 2 is often said to be
exponent
Moving the decimal point to the left
squared
0

21. 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
0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1
change both terms in order to keep the value the same.

22. 0 to any power is equal to
10^-1
0
When the exponent of a power-of-10 expression is a negative integer:
Because 4 multiplied by itself equals 16.

23. When you change the position of the decimal point in a coefficient value
exponent
When the exponent of a power-of-10 expression is a negative integer:
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.

24. What number multiplied by itself is equal to 16? The answer is 4. Why?
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.
Because 4 multiplied by itself equals 16.
1
10^2

25. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Scientific notation
Because 4 multiplied by itself equals 16.
Calculator square-root key
proper scientific

26. 5^1 =
1. Multiply the coefficients 2. Add the exponents
0
1. Divide the coefficients 2. Subtract the exponents
5

27. To find the square root of any number - simply key in the number (the radicand) and press the
1. Divide the coefficients 2. Subtract the exponents
Same 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
Calculator square-root key

28. A number is a second number which - when multiplied by itself three times - equals the original number.
The solution exists - but not in the real number system.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
negative number
cube root

29. Any number with an exponent of 0 is equal to
1. Multiply the coefficients 2. Add the exponents
Subtract the exponent
itself
1

30. 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.
Engineering notation
When moving the decimal point to the left (dividing by 10)
2
exponent

31. 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
perfect square
When moving the decimal point to the left (dividing by 10)
Are Equal
cube-root key

32. 100 - or 1 with the decimal point moved two places to the right
9 (3^2 = 9)
10^2
6.74 x 10^-7
1 divided by that number with a positive exponent

33. 1^4 =
1
Calculator square-root key
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.
Engineering notation

34. 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.
0
same exponent
perfect square
10^1

35. 10 - or 1 with the decimal point moved one place to the right
base
1. Multiply the coefficients 2. Add the exponents
2 x 10^9
10^1

36. 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
change both terms in order to keep the value the same.
cube root
0
same exponent

37. Always 10 for scientific notation
0
base
itself
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

38. Indicates the number of times the base is to be multiplied.
Moving the decimal point to the left
Subtract the exponent
exponent
change both terms in order to keep the value the same.

39. The cube root of zero is
10^2
0
Scientific notation
The solution exists - but not in the real number system.

40. A number with an exponent of 3 is often said to be
cube root
cubed
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1. Divide the coefficients 2. Subtract the exponents

41. Valid powers of 10 for engineering notation are:
negative number
0
Not
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

42. To add powers of ten:
9 (3^2 = 9)
decrease the power-of-10 exponent by the same number of units
adjust the value of the coefficient
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

43. A number - when multiplied by itself - is equal to a given number.
To multiply powers that have the same base:
cube-root key
exponent
square root

44. The decimal part
one digit to the left of the decimal point
coefficient
1
1

45. The square root of 9 is
Moving the decimal point to the left
2
3
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

46. 1 to any power is equal to
0
must be multiples of 3 or 0
1
a fractional decimal

47. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
coefficient
2
the radical sign with a little 3 that indicates the cube root:
5

48. 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.
1
Not
1. Divide the coefficients 2. Subtract the exponents
When the exponent of a power-of-10 expression is a negative integer:

49. There are no special rules for adding and subtracting numbers that are written with exponents.
radical sign
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
9 (3^2 = 9)

50. 3^0 =
1
a fractional decimal
Not
Are Equal