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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. A number is a second number which - when multiplied by itself three times - equals the original number.
Calculator square-root key
base
When moving the decimal point to the left (dividing by 10)
cube root

2. 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.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1
a fractional decimal

3. 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.
proper scientific
itself
perfect square
1

4. When you decrease the value of the power-of-10 exponent
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.
move the decimal point the same number of units to the right
Moving the decimal point to the left
move the decimal point the same number of units to the left

5. The square root of zero is
10^-2
Moving the decimal point to the left
Because 4 multiplied by itself equals 16.
0

6. When the exponents are not the same
Are Equal
move the decimal point the same number of units to the right
rewrite one of the terms so that the exponents are equal
5

7. Step 1: Add the exponents Step 2: Use the common base
Scientific notation
To multiply powers that have the same base:
Moving the decimal point to the right
decrease the value of the exponent by 1 (dividing by 10)

8. 0^5 =
move the decimal point the same number of units to the right
2
0
one digit to the left of the decimal point

9. = 0.1 - or 1 with the decimal point moved one place to the left.
Scientific notation
10^-1
cube root
base

10. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
the radical sign with a little 3 that indicates the cube root:
Because 4 multiplied by itself equals 16.
decrease the value of the exponent by 1 (dividing by 10)

11. Indicates the number of times the base is to be multiplied.
exponent
Not
rewrite one of the terms so that the exponents are equal
negative number

12.
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
The solution exists - but not in the real number system.
must be multiples of 3 or 0
Calculator square-root key

13. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
To multiply powers that have the same base:
same exponent
cube-root key

14. The cube root of a negative number is also a
square root
6.74 x 10^-7
negative number
must be multiples of 3 or 0

15. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1. Divide the coefficients 2. Subtract the exponents
base
2
change both terms in order to keep the value the same.

16. When you move the decimal point in the coefficient to the right
rewrite one of the terms so that the exponents are equal
decrease the power-of-10 exponent by the same number of units
0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

17. Don't bother trying to find the square root of a negative number.
Same base
radical sign
The solution exists - but not in the real number system.
2 x 10^9

18. = 0.01 - or 1 with the decimal point moved two places to the left.
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Step 1. Divide the coefficients of the terms
10^-2

19. Increase the value of the exponent by 1 (multiplying by 10)
itself
When moving the decimal point to the left (dividing by 10)
the radical sign with a little 3 that indicates the cube root:
decrease the power-of-10 exponent by the same number of units

20. When moving the decimal point to the right (multiplying by 10)
Calculator square-root key
1 divided by that number with a positive exponent
1
decrease the value of the exponent by 1 (dividing by 10)

21. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Engineering notation
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
2 x 10^9
negative number

22. The decimal part
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Subtract the exponent
coefficient
Moving the decimal point to the right

23. Negative cube roots are okay ... negative square roots are
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
base
Not
2

24. A number - when multiplied by itself - is equal to a given number.
you have to adjust the value of the exponent in order avoid changing the actual value.
perfect square
1
square root

25. 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
coefficient
decrease the value of the exponent by 1 (dividing by 10)
cubed

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.
10^2
one digit to the left of the decimal point
0
radical sign

27. Multiplying by 10
Moving the decimal point to the right
Engineering notation
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

28. To divide powers of ten:
When moving the decimal point to the left (dividing by 10)
must be multiples of 3 or 0
1. Divide the coefficients 2. Subtract the exponents
decrease the value of the exponent by 1 (dividing by 10)

29. To add powers of ten:
Scientific notation
base
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1

30. What number multiplied by itself is equal to 16? The answer is 4. Why?
When the exponent of a power-of-10 expression is a negative integer:
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.
Subtract the exponent
Because 4 multiplied by itself equals 16.

31. Scientific notation requires there to be only
one digit to the left of the decimal point
1
0
base

32. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
1
To multiply powers that have the same base:
10^2

33. To find the square root of any number - simply key in the number (the radicand) and press the
10^-18
Calculator square-root key
adjust the value of the coefficient
perfect square

34. Powers of ten can be added or subtracted only when their exponents
perfect square
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Are Equal
1 divided by that number with a positive exponent

35. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
negative number
the radical sign with a little 3 that indicates the cube root:
base

36. 1 to any power is equal to
10^1
1
move the decimal point the same number of units to the right
rewrite one of the terms so that the exponents are equal

37. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
move the decimal point the same number of units to the left
The solution exists - but not in the real number system.
2 x 10^9

38. 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
change both terms in order to keep the value the same.
increase the power-of-10 exponent by the same number of units
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
you have to adjust the value of the exponent in order avoid changing the actual value.

39. Any number with an exponent of 0 is equal to
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
base
1
change both terms in order to keep the value the same.

40. To multiply powers of 10:
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.
5
1. Multiply the coefficients 2. Add the exponents
3

41. When you move the decimal point in the coefficient to the left
1. Divide the coefficients 2. Subtract the exponents
increase the power-of-10 exponent by the same number of units
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
squared

42. Always 10 for scientific notation
1. Multiply the coefficients 2. Add the exponents
a fractional decimal
rewrite one of the terms so that the exponents are equal
base

43. 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:
negative number
cube root
2

44. 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
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
rewrite one of the terms so that the exponents are equal
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

45. 1 to any power is equal to
Not
1
decrease the power-of-10 exponent by the same number of units
5

46. Any number with an exponent of 1 is equal to
Engineering notation
itself
Subtract the exponent
exponent

47. A very small number such as 0.000000674 can be written with scientific notation as
square root
must be multiples of 3 or 0
6.74 x 10^-7
1

48. To divide powers of 10:
1 divided by that number with a positive exponent
Step 1. Divide the coefficients of the terms
0
move the decimal point the same number of units to the right

49. To multiply powers of ten:
move the decimal point the same number of units to the left
1. Multiply the coefficients 2. Add the exponents
10^1
move the decimal point the same number of units to the right

50. To subtract powers of ten:
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
To multiply powers that have the same base:
proper scientific