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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 reenforces your understanding as you take the test each time.
1. When moving the decimal point to the right (multiplying by 10)
10^2
change both terms in order to keep the value the same.
decrease the value of the exponent by 1 (dividing by 10)
the radical sign with a little 3 that indicates the cube root:
2. 1 to any power is equal to
change both terms in order to keep the value the same.
1
Because the exponent for the base10 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
0
3. 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.
must be multiples of 3 or 0
decrease the value of the exponent by 1 (dividing by 10)
When the exponent of a powerof10 expression is a negative integer:
0
4. A number is a second number which  when multiplied by itself three times  equals the original number.
base
0
cube root
Step 1. Divide the coefficients of the terms
5. 100  or 1 with the decimal point moved two places to the right
Not
10^2
10^1
Subtract the exponent
6. 0 to any power is equal to
To multiply powers that have the same base:
0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Because the exponent for the base10 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
7. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
squared
exponent
increase the powerof10 exponent by the same number of units
8. 10  or 1 with the decimal point moved one place to the right
Are Equal
cubed
exponent
10^1
9. Negative cube roots are okay ... negative square roots are
radical sign
Step 1. Divide the coefficients of the terms
Not
Are Equal
10. Any number with a negative exponent is equal to
adjust the value of the coefficient
decrease the value of the exponent by 1 (dividing by 10)
9 (3^2 = 9)
1 divided by that number with a positive exponent
11. Scientific notation requires there to be only
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Because 4 multiplied by itself equals 16.
one digit to the left of the decimal point
Moving the decimal point to the left
12. 5^1 =
Moving the decimal point to the left
move the decimal point the same number of units to the right
5
Scientific notation
13. A negative exponent does not mean the decimal value is negative. It means the decimal value is
1
10^18
one digit to the left of the decimal point
a fractional decimal
14. 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
adjust the value of the coefficient
1
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.
15. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^7
Not
one digit to the left of the decimal point
1
16. 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
Each number must first be converted to its ordinary decimal form  then complete the addition/subtraction operation.
Engineering notation
Step 1. Divide the coefficients of the terms
same exponent
17. To divide powers of ten:
5
1. Divide the coefficients 2. Subtract the exponents
When the exponent of a powerof10 expression is a negative integer:
Each number must first be converted to its ordinary decimal form  then complete the addition/subtraction operation.
18. The square of 3 is
10^2
0
9 (3^2 = 9)
0
19. To divide powers that have the same base:
0
10^2
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
cubed
20. Valid powersof10 for engineering notation
Not
Same base
Subtract the exponent
must be multiples of 3 or 0
21. 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.
adjust the value of the coefficient
decrease the value of the exponent by 1 (dividing by 10)
1
radical sign
22. When you move the decimal point in the coefficient to the left
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
radical sign
increase the powerof10 exponent by the same number of units
23. Don't bother trying to find the square root of a negative number.
Are Equal
Moving the decimal point to the right
0
The solution exists  but not in the real number system.
24. Because the exponent for the base10 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
10^2
Because the exponent for the base10 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
1
rewrite one of the terms so that the exponents are equal
25. To multiply powers of ten:
Subtract the exponent
0
the radical sign with a little 3 that indicates the cube root:
1. Multiply the coefficients 2. Add the exponents
26. A number with an exponent of 2 is often said to be
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
squared
2
0
27. There are no special rules for adding and subtracting numbers that are written with exponents.
Step 1. Divide the coefficients of the terms
Scientific notation
Each number must first be converted to its ordinary decimal form  then complete the addition/subtraction operation.
radical sign
28. Indicates the number to be multiplied.
Because 4 multiplied by itself equals 16.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
5
base
29. The square root of 9 is
Moving the decimal point to the left
2 x 10^9
proper scientific
3
30. To find the square root of any number  simply key in the number (the radicand) and press the
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
When the exponent of a powerof10 expression is a negative integer:
Calculator squareroot key
10^3 10^6 10^9 10^ 3 10^ 6 10^ 9 10^0
31. The decimal part
5
coefficient
square root
Moving the decimal point to the left
32. A number  when multiplied by itself  is equal to a given number.
rewrite one of the terms so that the exponents are equal
square root
move the decimal point the same number of units to the left
1
33. To add powers of ten:
exponent
5
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 right
34. The symbol for the cube root of a number is
Same base
0
Subtract the exponent
the radical sign with a little 3 that indicates the cube root:
35. Powers of ten can be added or subtracted only when their exponents
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.
square root
Are Equal
base
36. Dividing by 10
one digit to the left of the decimal point
Moving the decimal point to the left
10^1
squared
37. 3^0 =
10^1
1
cubed
radical sign
38.
Determine the number of times the original decimal has to be multiplied or divided by 10 in order to show one nonzero digit to the left of the decimal point. Multiply the normalized value by a power of 10 that will restore equality. If you multiplie
decrease the value of the exponent by 1 (dividing by 10)
squared
3
39. Multiplying by 10
Because 4 multiplied by itself equals 16.
Moving the decimal point to the right
cuberoot key
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
40. When you decrease the value of the powerof10 exponent
decrease the value of the exponent by 1 (dividing by 10)
1. Divide the coefficients 2. Subtract the exponents
move the decimal point the same number of units to the right
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
41. When you increase the value of the powerof10 exponent
1
10^2
square root
move the decimal point the same number of units to the left
42. To multiply powers of 10:
9 (3^2 = 9)
rewrite one of the terms so that the exponents are equal
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
43. Increase the value of the exponent by 1 (multiplying by 10)
When the exponent of a powerof10 expression is a negative integer:
decrease the value of the exponent by 1 (dividing by 10)
rewrite one of the terms so that the exponents are equal
When moving the decimal point to the left (dividing by 10)
44. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
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.
0
Subtract the exponent
45. A number with an exponent of 3 is often said to be
Scientific notation
cubed
1. Multiply the coefficients 2. Add the exponents
move the decimal point the same number of units to the left
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
you have to adjust the value of the exponent in order avoid changing the actual value.
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.
change both terms in order to keep the value the same.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
47. 1^4 =
1
coefficient
Moving the decimal point to the right
exponent
48. 0^5 =
exponent
0
change both terms in order to keep the value the same.
Engineering notation
49. A very large number such as 2 000 000 000 can be written with scientific notation as
perfect square
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
2 x 10^9
50. To subtract powers of ten:
Subtract the exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Each number must first be converted to its ordinary decimal form  then complete the addition/subtraction operation.
1