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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. The square root of zero is
0
9 (3^2 = 9)
Subtract the exponent
Scientific notation

2. Valid powers of 10 for engineering notation are:
Calculator square-root key
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
cubed
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

3. 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
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1. Multiply the coefficients 2. Add the exponents
same exponent
adjust the value of the coefficient

4. Any number with a negative exponent is equal to
itself
1. Multiply the coefficients 2. Add the exponents
1 divided by that number with a positive exponent
10^-2

5. 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
the radical sign with a little 3 that indicates the cube root:
1
1. Divide the coefficients 2. Subtract the exponents

6. Indicates the number of times the base is to be multiplied.
rewrite one of the terms so that the exponents are equal
10^1
The solution exists - but not in the real number system.
exponent

7. Any number with an exponent of 1 is equal to
perfect square
adjust the value of the coefficient
itself
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

8. The square root of 9 is
3
To multiply powers that have the same base:
1
2 x 10^9

9. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
1. Multiply the coefficients 2. Add the exponents
Subtract the exponent
exponent
radical sign

10. A negative exponent does not mean the decimal value is negative. It means the decimal value is
itself
a fractional decimal
move the decimal point the same number of units to the right
Scientific notation

11. When you change the position of the decimal point in a coefficient value
perfect square
1
you have to adjust the value of the exponent in order avoid changing the actual value.
1

12. 1 to any power is equal to
10^2
Moving the decimal point to the left
9 (3^2 = 9)
1

13. When you move the decimal point in the coefficient to the left
Because 4 multiplied by itself equals 16.
The solution exists - but not in the real number system.
10^-1
increase the power-of-10 exponent by the same number of units

14. Multiplying by 10
increase the power-of-10 exponent by the same number of units
1 divided by that number with a positive exponent
Moving the decimal point to the right
5

15. 3^0 =
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
proper scientific
1
negative number

16. To add or subtract numbers written with exponents:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
must be multiples of 3 or 0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Because 4 multiplied by itself equals 16.

17. 10 - or 1 with the decimal point moved one place to the right
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
Moving the decimal point to the left
squared
10^1

18. The square of 3 is
1
9 (3^2 = 9)
squared
cube root

19. When you move the decimal point in the coefficient to the right
same exponent
perfect square
0
decrease the power-of-10 exponent by the same number of units

20. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
0
Calculator square-root key
2 x 10^9
Moving the decimal point to the right

21. When you increase the value of the power-of-10 exponent
coefficient
perfect square
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the left

22. What number multiplied by itself is equal to 16? The answer is 4. Why?
1
Because 4 multiplied by itself equals 16.
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
Step 1. Divide the coefficients of the terms

23. There are no special rules for adding and subtracting numbers that are written with exponents.
The solution exists - but not in the real number system.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
base
one digit to the left of the decimal point

24. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
Scientific notation
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
square root

25. For the 10
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
exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the left

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.
Because 4 multiplied by itself equals 16.
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
radical sign

27. To divide powers of ten:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
coefficient
1. Divide the coefficients 2. Subtract the exponents
cube-root key

28. The symbol for the cube root of a number is
Moving the decimal point to the left
cubed
must be multiples of 3 or 0
the radical sign with a little 3 that indicates the cube root:

29. To add powers of ten:
one digit to the left of the decimal point
decrease the value of the exponent by 1 (dividing by 10)
10^1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

30. 1 to any power is equal to
1
exponent
Step 1. Divide the coefficients of the terms
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

31. Any number with an exponent of 0 is equal to
1 divided by that number with a positive exponent
the radical sign with a little 3 that indicates the cube root:
1
exponent

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

33. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
square root
you have to adjust the value of the exponent in order avoid changing the actual value.
Scientific notation

34. A number - when multiplied by itself - is equal to a given number.
coefficient
square root
itself
cube-root key

35. Scientific notation requires there to be only
one digit to the left of the decimal point
0
6.74 x 10^-7
move the decimal point the same number of units to the right

36. A number with an exponent of 3 is often said to be
one digit to the left of the decimal point
cubed
increase the power-of-10 exponent by the same number of units
move the decimal point the same number of units to the right

37. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-1
Because 4 multiplied by itself equals 16.
Subtract the exponent
10^-2

38. 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.
Scientific notation
0
10^-2
proper scientific

39. 100 - or 1 with the decimal point moved two places to the right
10^2
you have to adjust the value of the exponent in order avoid changing the actual value.
exponent
6.74 x 10^-7

40. The decimal part
coefficient
Scientific notation
The solution exists - but not in the real number system.
10^2

41. When you decrease the value of the power-of-10 exponent
the radical sign with a little 3 that indicates the cube root:
move the decimal point the same number of units to the right
Same base
adjust the value of the coefficient

42. Indicates the number to be multiplied.
exponent
base
Moving the decimal point to the left
rewrite one of the terms so that the exponents are equal

43. Powers of ten can be added or subtracted only when their exponents
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-2
radical sign
Are Equal

44. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
coefficient
Engineering notation
2
Same base

45. Always 10 for scientific notation
base
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
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

46. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
2
itself
proper scientific
rewrite one of the terms so that the exponents are equal

47. Step 1: Add the exponents Step 2: Use the common base
itself
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
base
To multiply powers that have the same base:

48. = 0.1 - or 1 with the decimal point moved one place to the left.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^-1
1
Engineering notation

49. 0 to any power is equal to
5
0
Scientific notation
decrease the value of the exponent by 1 (dividing by 10)

50. 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.
10^-2
negative number
1
perfect square