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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. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
move the decimal point the same number of units to the right
proper scientific
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 right

2. When the exponents are not the same
must be multiples of 3 or 0
rewrite one of the terms so that the exponents are equal
Same base
decrease the power-of-10 exponent by the same number of units

3. 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
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
one digit to the left of the decimal point
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
squared

4. The decimal part
Moving the decimal point to the right
0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
coefficient

5. Indicates the number to be multiplied.
Not
base
coefficient
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

6. The cube root of a negative number is also a
negative number
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Scientific notation
exponent

7. A very small number such as 0.000000674 can be written with scientific notation as
Are Equal
0
6.74 x 10^-7
Moving the decimal point to the right

8. 10 - or 1 with the decimal point moved one place to the right
radical sign
squared
5
10^1

9. Don't bother trying to find the square root of a negative number.
Calculator square-root key
The solution exists - but not in the real number system.
negative number
0

10. 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.
Scientific notation
1. Divide the coefficients 2. Subtract the exponents
When the exponent of a power-of-10 expression is a negative integer:
you have to adjust the value of the exponent in order avoid changing the actual value.

11. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
adjust the value of the coefficient
2 x 10^9
base
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

12. Any number with an exponent of 0 is equal to
rewrite one of the terms so that the exponents are equal
must be multiples of 3 or 0
1
Are Equal

13. Multiplying by 10
5
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.
Moving the decimal point to the right

14. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
1 divided by that number with a positive exponent
10^2
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

15. 1^4 =
5
Are Equal
1
9 (3^2 = 9)

16. 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
3
adjust the value of the coefficient
Scientific notation

17. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
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
1. Multiply the coefficients 2. Add the exponents
0

18. What number multiplied by itself is equal to 16? The answer is 4. Why?
exponent
move the decimal point the same number of units to the left
10^-18
Because 4 multiplied by itself equals 16.

19. Indicates the number of times the base is to be multiplied.
Same base
1
0
exponent

20. The square root of 9 is
decrease the power-of-10 exponent by the same number of units
a fractional decimal
increase the power-of-10 exponent by the same number of units
3

21. There are no special rules for adding and subtracting numbers that are written with exponents.
When the exponent of a power-of-10 expression is a negative integer:
squared
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
3

22. Numbers with exponents can be directly multiplied or divided only when they have the
cubed
move the decimal point the same number of units to the left
Same base
Calculator square-root key

23. 1 to any power is equal to
1
10^1
base
The solution exists - but not in the real number system.

24. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
1 divided by that number with a positive exponent
The solution exists - but not in the real number system.
1

25. 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
1
move the decimal point the same number of units to the left
Because 4 multiplied by itself equals 16.

26. 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
1
adjust the value of the coefficient
5
negative number

27. 100 - or 1 with the decimal point moved two places to the right
10^-1
10^2
same exponent
Subtract the exponent

28. Scientific notation requires there to be only
0
exponent
The solution exists - but not in the real number system.
one digit to the left of the decimal point

29. 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.
radical sign
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
10^-18
Engineering notation

30. To add powers of ten:
one digit to the left of the decimal point
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
When the exponent of a power-of-10 expression is a negative integer:
rewrite one of the terms so that the exponents are equal

31. To divide powers of 10:
Step 1. Divide the coefficients of the terms
move the decimal point the same number of units to the right
9 (3^2 = 9)
10^-2

32. A number with an exponent of 3 is often said to be
To multiply powers that have the same base:
cubed
decrease the value of the exponent by 1 (dividing by 10)
2 x 10^9

33. A number - when multiplied by itself - is equal to a given number.
decrease the power-of-10 exponent by the same number of units
Step 1. Divide the coefficients of the terms
When the exponent of a power-of-10 expression is a negative integer:
square root

34. The symbol for the cube root of a number is
1
radical sign
the radical sign with a little 3 that indicates the cube root:
1

35. To multiply powers of 10:
one digit to the left of the decimal point
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.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
exponent

36. When you increase the value of the power-of-10 exponent
radical sign
Moving the decimal point to the left
move the decimal point the same number of units to the left
move the decimal point the same number of units to the right

37. 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
1
change both terms in order to keep the value the same.
5
10^-2

38. The square of 3 is
10^-2
exponent
9 (3^2 = 9)
10^-18

39. 5^1 =
cube-root key
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
5
coefficient

40. Any number with an exponent of 1 is equal to
Not
itself
9 (3^2 = 9)
Calculator square-root key

41. The cube root of zero is
0
base
Subtract the exponent
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

42. To divide powers of ten:
1
1. Divide the coefficients 2. Subtract the exponents
Because 4 multiplied by itself equals 16.
rewrite one of the terms so that the exponents are equal

43. To add or subtract numbers written with exponents:
0
one digit to the left of the decimal point
1. Multiply the coefficients 2. Add the exponents
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

44. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
proper scientific
Because 4 multiplied by itself equals 16.
0

45. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
The solution exists - but not in the real number system.
square root
10^-1

46. 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.
The solution exists - but not in the real number system.
Because 4 multiplied by itself equals 16.
proper scientific

47. Powers of ten can be added or subtracted only when their exponents
10^2
Are Equal
0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

48. 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
cubed
cube-root key
Subtract the exponent
proper scientific

49. 0^5 =
exponent
Moving the decimal point to the left
0
Step 1. Divide the coefficients of the terms

50. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
Not
10^-2
cubed