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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. 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.
change both terms in order to keep the value the same.
Scientific notation
1
To multiply powers that have the same base:

2. = 0.1 - or 1 with the decimal point moved one place to the left.
exponent
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^-1
3

3. 3^0 =
1 divided by that number with a positive exponent
6.74 x 10^-7
Engineering notation
1

4. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
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
1. Divide the coefficients 2. Subtract the exponents
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

5. Scientific notation requires there to be only
one digit to the left of the decimal point
cubed
square root
negative number

6. A number with an exponent of 2 is often said to be
coefficient
adjust the value of the coefficient
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
squared

7. To divide powers of ten:
itself
1. Divide the coefficients 2. Subtract the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.
a fractional decimal

8. Any number with an exponent of 0 is equal to
3
the radical sign with a little 3 that indicates the cube root:
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

9. To find the square root of any number - simply key in the number (the radicand) and press the
9 (3^2 = 9)
Calculator square-root key
1. Divide the coefficients 2. Subtract the exponents
0

10. Any number with an exponent of 1 is equal to
itself
a fractional decimal
the radical sign with a little 3 that indicates the cube root:
1

11. Powers of ten can be added or subtracted only when their exponents
6.74 x 10^-7
cube root
Are Equal
a fractional decimal

12. 1 to any power is equal to
radical sign
Subtract the exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1

13. A number - when multiplied by itself - is equal to a given number.
cubed
5
square root
0

14. A very small number such as 0.000000674 can be written with scientific notation as
move the decimal point the same number of units to the right
9 (3^2 = 9)
6.74 x 10^-7
2 x 10^9

15. 5^1 =
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Are Equal
10^-2
5

16. When you increase the value of the power-of-10 exponent
The solution exists - but not in the real number system.
move the decimal point the same number of units to the left
0
cube root

17. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
1 divided by that number with a positive exponent
cubed
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

18. To subtract powers of ten:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
negative number

19. 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
5
you have to adjust the value of the exponent in order avoid changing the actual value.
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
The solution exists - but not in the real number system.

20. Always 10 for scientific notation
Step 1. Divide the coefficients of the terms
10^2
base
square root

21. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
Same base
2
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

22. 0 to any power is equal to
you have to adjust the value of the exponent in order avoid changing the actual value.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
0

23. = 0.01 - or 1 with the decimal point moved two places to the left.
Scientific notation
10^-2
exponent
cube root

24. Negative cube roots are okay ... negative square roots are
Subtract the exponent
When moving the decimal point to the left (dividing by 10)
Not
a fractional decimal

25. Indicates the number to be multiplied.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
base
exponent
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

26. To multiply powers of 10:
increase the power-of-10 exponent by the same number of units
Scientific notation
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

27. When you decrease the value of the power-of-10 exponent
squared
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
Not
move the decimal point the same number of units to the right

28. A number with an exponent of 3 is often said to be
The solution exists - but not in the real number system.
cubed
1. Multiply the coefficients 2. Add the exponents
one digit to the left of the decimal point

29. 100 - or 1 with the decimal point moved two places to the right
10^2
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
rewrite one of the terms so that the exponents are equal

30. Any number with a negative exponent is equal to
squared
1 divided by that number with a positive exponent
cube root
1

31. To add powers of ten:
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
proper scientific
1

32. Valid powers-of-10 for engineering notation
Subtract the exponent
negative number
one digit to the left of the decimal point
must be multiples of 3 or 0

33. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
one digit to the left of the decimal point
proper scientific
Step 1. Divide the coefficients of the terms
0

34.
Because 4 multiplied by itself equals 16.
Calculator square-root key
cube-root key
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

35. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
Scientific notation
rewrite one of the terms so that the exponents are equal
move the decimal point the same number of units to the left

36. The cube root of zero is
0
exponent
10^-2
cubed

37. The square root of zero is
0
decrease the value of the exponent by 1 (dividing by 10)
Subtract the exponent
same exponent

38. 10 - or 1 with the decimal point moved one place to the right
negative number
1
10^1
Are Equal

39. When you change the position of the decimal point in a coefficient value
you have to adjust the value of the exponent in order avoid changing the actual value.
When moving the decimal point to the left (dividing by 10)
2
0

40. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
0
change both terms in order to keep the value the same.
increase the power-of-10 exponent by the same number of units

41. 1^4 =
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
must be multiples of 3 or 0
squared
1

42. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
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.
one digit to the left of the decimal point

43. To divide powers that have the same base:
Moving the decimal point to the left
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
When the exponent of a power-of-10 expression is a negative integer:
decrease the power-of-10 exponent by the same number of units

44. 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
Because 4 multiplied by itself equals 16.
cube root
increase the power-of-10 exponent by the same number of units
adjust the value of the coefficient

45. 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
1 divided by that number with a positive exponent
you have to adjust the value of the exponent in order avoid changing the actual value.

46. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
move the decimal point the same number of units to the left
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
When moving the decimal point to the left (dividing by 10)

47. The square of 3 is
1 divided by that number with a positive exponent
9 (3^2 = 9)
10^-1
one digit to the left of the decimal point

48. There are no special rules for adding and subtracting numbers that are written with exponents.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

49. Indicates the number of times the base is to be multiplied.
move the decimal point the same number of units to the right
1. Multiply the coefficients 2. Add the exponents
rewrite one of the terms so that the exponents are equal
exponent

50. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
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