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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.
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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. Valid powers-of-10 for engineering notation
base
rewrite one of the terms so that the exponents are equal
must be multiples of 3 or 0
perfect square

2. Indicates the number of times the base is to be multiplied.
exponent
square root
6.74 x 10^-7
same exponent

3. The square root of zero is
0
Step 1. Divide the coefficients of the terms
3
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

4. Any number with a negative exponent is equal to
coefficient
1 divided by that number with a positive exponent
rewrite one of the terms so that the exponents are equal
The solution exists - but not in the real number system.

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
cube-root key
10^2
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

6. What number multiplied by itself is equal to 16? The answer is 4. Why?
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
Because 4 multiplied by itself equals 16.
increase the power-of-10 exponent by the same number of units

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
10^-2
Step 1. Divide the coefficients of the terms
squared

8. 3^0 =
1
exponent
The solution exists - but not in the real number system.
base

9. The decimal part
1
coefficient
square root
the radical sign with a little 3 that indicates the cube root:

10. 1^4 =
2
0
1
Moving the decimal point to the right

11. A number with an exponent of 2 is often said to be
squared
you have to adjust the value of the exponent in order avoid changing the actual value.
0
0

12. 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
Same base
change both terms in order to keep the value the same.
exponent
cube root

13. To divide powers of 10:
10^-18
perfect square
Step 1. Divide the coefficients of the terms
base

14. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
coefficient
2
10^1
radical sign

15. 0 to any power is equal to
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1. Multiply the coefficients 2. Add the exponents
0

16. To multiply or divide exponent terms that do not have the same base:
Not
The solution exists - but not in the real number system.
0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

17. Numbers with exponents can be directly multiplied or divided only when they have the
Same base
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
1

18. 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
cube-root key
1. Divide the coefficients 2. Subtract the exponents
0
radical sign

19. To find the square root of any number - simply key in the number (the radicand) and press the
one digit to the left of the decimal point
move the decimal point the same number of units to the left
Calculator square-root key
base

20. Negative cube roots are okay ... negative square roots are
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
adjust the value of the coefficient
Not
coefficient

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

22. For the 10
1
base
exponent
9 (3^2 = 9)

23. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Are Equal
5
a fractional decimal
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

24. The square root of 9 is
one digit to the left of the decimal point
3
itself
0

25. 10 - or 1 with the decimal point moved one place to the right
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
10^1
Are Equal
adjust the value of the coefficient

26. To divide powers of ten:
2 x 10^9
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the right
1. Divide the coefficients 2. Subtract the exponents

27. To multiply powers of ten:
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.
0
1. Multiply the coefficients 2. Add the exponents

28. = 0.1 - or 1 with the decimal point moved one place to the left.
one digit to the left of the decimal point
10^-1
square root
base

29. 1 to any power is equal to
When moving the decimal point to the left (dividing by 10)
0
1 divided by that number with a positive exponent
1

30. 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.
increase the power-of-10 exponent by the same number of units
5
Engineering notation
When moving the decimal point to the left (dividing by 10)

31. When moving the decimal point to the right (multiplying by 10)
move the decimal point the same number of units to the right
negative number
2 x 10^9
decrease the value of the exponent by 1 (dividing by 10)

32. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^-2
1
9 (3^2 = 9)

33. Step 1: Add the exponents Step 2: Use the common base
10^-1
To multiply powers that have the same base:
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.

34. 0^5 =
Subtract the exponent
0
perfect square
2

35. 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.
2
adjust the value of the coefficient
Scientific notation
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

36. To multiply powers of 10:
cube-root key
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.
Moving the decimal point to the right

37. Represents 1 preceded by 17 zeros and a decimal point.
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^-18
9 (3^2 = 9)
1 divided by that number with a positive exponent

38. The cube root of zero is
0
Calculator square-root key
1. Divide the coefficients 2. Subtract the exponents
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

39. When you decrease the value of the power-of-10 exponent
2 x 10^9
exponent
cube-root key
move the decimal point the same number of units to the right

40. 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
Calculator square-root key
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
decrease the power-of-10 exponent by the same number of units
move the decimal point the same number of units to the left

41. A number - when multiplied by itself - is equal to a given number.
Moving the decimal point to the left
Not
increase the power-of-10 exponent by the same number of units
square root

42. The square of 3 is
9 (3^2 = 9)
10^-1
must be multiples of 3 or 0
The solution exists - but not in the real number system.

43. Dividing by 10
Moving the decimal point to the left
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Not
the radical sign with a little 3 that indicates the cube root:

44. Indicates the number to be multiplied.
10^1
base
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:

45. Any number with an exponent of 1 is equal to
must be multiples of 3 or 0
base
itself
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

46. Powers of ten can be added or subtracted only when their exponents
squared
change both terms in order to keep the value the same.
Are Equal
a fractional decimal

47. The symbol for the cube root of a number is
0
To multiply powers that have the same base:
the radical sign with a little 3 that indicates the cube root:
proper scientific

48. 1 to any power is equal to
1. Multiply the coefficients 2. Add the exponents
1
base
Are Equal

49. Any number with an exponent of 0 is equal to
must be multiples of 3 or 0
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
6.74 x 10^-7

50. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1. Multiply the coefficients 2. Add the exponents
must be multiples of 3 or 0
6.74 x 10^-7