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Test your basic knowledge |
CLEP General Mathematics: Powers Exponents And Roots
Start Test
Study First
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. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
2. 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.
cube root
Engineering notation
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
When moving the decimal point to the left (dividing by 10)
3. A very small number such as 0.000000674 can be written with scientific notation as
10^2
1. Multiply the coefficients 2. Add the exponents
6.74 x 10^-7
Engineering notation
4. When you decrease the value of the power-of-10 exponent
radical sign
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
move the decimal point the same number of units to the right
must be multiples of 3 or 0
5. A number - when multiplied by itself - is equal to a given number.
same exponent
Moving the decimal point to the right
square root
6.74 x 10^-7
6. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
0
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
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Subtract the exponent
7. Always 10 for scientific notation
the radical sign with a little 3 that indicates the cube root:
one digit to the left of the decimal point
base
coefficient
8. 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.
perfect square
adjust the value of the coefficient
The solution exists - but not in the real number system.
radical sign
9. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
cubed
1
Step 1. Divide the coefficients of the terms
10. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
squared
10^-1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
11. Scientific notation requires there to be only
When the exponent of a power-of-10 expression is a negative integer:
2 x 10^9
cube root
one digit to the left of the decimal point
12. There are no special rules for adding and subtracting numbers that are written with exponents.
base
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Engineering notation
1
13. 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.
When the exponent of a power-of-10 expression is a negative integer:
10^-18
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
0
14. The cube root of zero is
the radical sign with a little 3 that indicates the cube root:
square root
Scientific notation
0
15. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
proper scientific
squared
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
2
16. Any number with an exponent of 1 is equal to
10^2
10^-2
Calculator square-root key
itself
17. The decimal part
squared
coefficient
exponent
cubed
18. Any number with an exponent of 0 is equal to
a fractional decimal
2
1
3
19. To add or subtract numbers written with exponents:
10^2
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Because 4 multiplied by itself equals 16.
20. When you increase the value of the power-of-10 exponent
decrease the value of the exponent by 1 (dividing by 10)
base
Step 1. Divide the coefficients of the terms
move the decimal point the same number of units to the left
21. Negative cube roots are okay ... negative square roots are
cube-root key
radical sign
When moving the decimal point to the left (dividing by 10)
Not
22. 0^5 =
exponent
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
0
23. A number with an exponent of 2 is often said to be
squared
increase the power-of-10 exponent by the same number of units
square root
one digit to the left of the decimal point
24. 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
2 x 10^9
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
5
0
25. 1^4 =
proper scientific
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
6.74 x 10^-7
1
26. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
square root
decrease the power-of-10 exponent by the same number of units
proper scientific
1 divided by that number with a positive exponent
27. The square root of zero is
5
0
perfect square
Same base
28. To add powers of ten:
9 (3^2 = 9)
Not
negative number
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
29. To subtract powers of ten:
10^1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
adjust the value of the coefficient
exponent
30. 3^0 =
1. Multiply the coefficients 2. Add the exponents
squared
a fractional decimal
1
31. 10 - or 1 with the decimal point moved one place to the right
10^1
cube root
Not
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
32. To divide powers of 10:
perfect square
move the decimal point the same number of units to the left
Step 1. Divide the coefficients of the terms
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
33. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
To multiply powers that have the same base:
move the decimal point the same number of units to the right
34. To divide powers of ten:
Are Equal
1. Divide the coefficients 2. Subtract the exponents
1
the radical sign with a little 3 that indicates the cube root:
35. = 0.01 - or 1 with the decimal point moved two places to the left.
must be multiples of 3 or 0
you have to adjust the value of the exponent in order avoid changing the actual value.
Not
10^-2
36. 0 to any power is equal to
Step 1. Divide the coefficients of the terms
Scientific notation
0
The solution exists - but not in the real number system.
37. Valid powers of 10 for engineering notation are:
squared
10^-2
base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
38. Multiplying by 10
10^-1
move the decimal point the same number of units 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
Moving the decimal point to the right
39. Valid powers-of-10 for engineering notation
coefficient
9 (3^2 = 9)
must be multiples of 3 or 0
1
40. To multiply powers of ten:
Scientific notation
1. Multiply the coefficients 2. Add the exponents
exponent
When moving the decimal point to the left (dividing by 10)
41. Any number with a negative exponent is equal to
increase the power-of-10 exponent by the same number of units
1 divided by that number with a positive exponent
move the decimal point the same number of units to the right
6.74 x 10^-7
42. The cube root of a negative number is also a
The solution exists - but not in the real number system.
1. Divide the coefficients 2. Subtract the exponents
a fractional decimal
negative number
43. 5^1 =
5
9 (3^2 = 9)
1
10^1
44. 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.
squared
Scientific notation
decrease the value of the exponent by 1 (dividing by 10)
one digit to the left of the decimal point
45. Dividing by 10
1
change both terms in order to keep the value the same.
Moving the decimal point to the left
move the decimal point the same number of units to the left
46. Indicates the number to be multiplied.
10^1
base
0
itself
47. A number with an exponent of 3 is often said to be
cubed
0
radical sign
10^2
48. Indicates the number of times the base is to be multiplied.
10^2
exponent
Step 1. Divide the coefficients of the terms
1 divided by that number with a positive exponent
49.
cube root
adjust the value of the coefficient
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
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
50. 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
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
The solution exists - but not in the real number system.
Step 1. Divide the coefficients of the terms
same exponent