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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. Dividing by 10
Moving the decimal point to the left
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
5
Subtract the exponent

2. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
decrease the power-of-10 exponent by the same number of units
2 x 10^9
decrease the value of the exponent by 1 (dividing by 10)
square root

3. 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
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
rewrite one of the terms so that the exponents are equal
adjust the value of the coefficient
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

4. Powers of ten can be added or subtracted only when their exponents
base
Subtract the exponent
6.74 x 10^-7
Are Equal

5. When you move the decimal point in the coefficient to the right
Step 1. Divide the coefficients of the terms
When moving the decimal point to the left (dividing by 10)
0
decrease the power-of-10 exponent by the same number of units

6. Multiplying by 10
Are Equal
base
The solution exists - but not in the real number system.
Moving the decimal point to the right

7. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
0
5
10^-18

8. A negative exponent does not mean the decimal value is negative. It means the decimal value is
cubed
cube-root key
a fractional decimal
1

9. To add powers of ten:
0
square root
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
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. Always 10 for scientific notation
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
negative number
base
radical sign

11. 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
Moving the decimal point 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
coefficient

12. To multiply or divide exponent terms that do not have the same base:
Step 1. Divide the coefficients of the terms
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

13. Valid powers-of-10 for engineering notation
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
must be multiples of 3 or 0
rewrite one of the terms so that the exponents are equal
cube root

14. When you change the position of the decimal point in a coefficient value
1
you have to adjust the value of the exponent in order avoid changing the actual value.
rewrite one of the terms so that the exponents are equal
perfect square

15. A number with an exponent of 3 is often said to be
When moving the decimal point to the left (dividing by 10)
Calculator square-root key
move the decimal point the same number of units to the right
cubed

16. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
Subtract the exponent
same exponent
must be multiples of 3 or 0

17. To divide powers of ten:
you have to adjust the value of the exponent in order avoid changing the actual value.
When the exponent of a power-of-10 expression is a negative integer:
Moving the decimal point to the right
1. Divide the coefficients 2. Subtract the exponents

18. Valid powers of 10 for engineering notation are:
Same base
1
1 divided by that number with a positive exponent
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

19. The square root of 9 is
coefficient
3
squared
10^-18

20. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Subtract the exponent
cube root

21. The square of 3 is
10^-18
Moving the decimal point to the right
Subtract the exponent
9 (3^2 = 9)

22. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Calculator square-root key
square root
proper scientific
1

23. 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
perfect square
Moving the decimal point to the right
Are Equal

24. A number with an exponent of 2 is often said to be
0
To multiply powers that have the same base:
squared
rewrite one of the terms so that the exponents are equal

25. To subtract powers of ten:
When moving the decimal point to the left (dividing by 10)
1
1. Multiply the coefficients 2. Add the exponents
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

26. The square root of zero is
Moving the decimal point to the right
0
3
1 divided by that number with a positive exponent

27. What number multiplied by itself is equal to 16? The answer is 4. Why?
exponent
0
base
Because 4 multiplied by itself equals 16.

28. Scientific notation requires there to be only
adjust the value of the coefficient
Scientific notation
one digit to the left of the decimal point
When moving the decimal point to the left (dividing by 10)

29. A number - when multiplied by itself - is equal to a given number.
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.
squared
square root
When moving the decimal point to the left (dividing by 10)

30. 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
radical sign
1. Divide the coefficients 2. Subtract the exponents
When the exponent of a power-of-10 expression is a negative integer:
cube-root key

31. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

32. To find the square root of any number - simply key in the number (the radicand) and press the
2 x 10^9
Calculator square-root key
10^2
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

33. Indicates the number of times the base is to be multiplied.
When moving the decimal point to the left (dividing by 10)
Because 4 multiplied by itself equals 16.
10^-18
exponent

34. 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.
the radical sign with a little 3 that indicates the cube root:
The solution exists - but not in the real number system.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

35. Numbers with exponents can be directly multiplied or divided only when they have the
a fractional decimal
10^-18
perfect square
Same base

36. Negative cube roots are okay ... negative square roots are
negative number
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
Not
5

37. 1 to any power is equal to
Moving the decimal point to the left
2 x 10^9
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.
1

38. To divide powers of 10:
Not
Step 1. Divide the coefficients of the terms
2 x 10^9
Are Equal

39. The cube root of zero is
negative number
itself
Are Equal
0

40. 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.
same exponent
Scientific notation
10^-18
a fractional decimal

41. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
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.
1
Step 1. Divide the coefficients of the terms

42. When moving the decimal point to the right (multiplying by 10)
Are Equal
decrease the value of the exponent by 1 (dividing by 10)
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
When moving the decimal point to the left (dividing by 10)

43. Any number with an exponent of 0 is equal to
To multiply powers that have the same base:
1
proper scientific
base

44. To multiply powers of 10:
you have to adjust the value of the exponent in order avoid changing the actual value.
itself
base
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.

45. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Moving the decimal point to the left
When the exponent of a power-of-10 expression is a negative integer:

46. Indicates the number to be multiplied.
1. Multiply the coefficients 2. Add the exponents
Same base
exponent
base

47. 100 - or 1 with the decimal point moved two places to the right
1 divided by that number with a positive exponent
Are Equal
10^2
coefficient

48. The cube root of a negative number is also a
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.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
negative number
perfect square

49. 10 - or 1 with the decimal point moved one place to the right
negative number
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
10^-18
10^1

50. 0 to any power is equal to
1
1
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
0