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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. 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.
Moving the decimal point to the right
must be multiples of 3 or 0
perfect square
Subtract the exponent

2. 1 to any power is equal to
exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

3. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
2
proper scientific
0
1

4. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
exponent
5
10^-18

5. To subtract powers of ten:
2 x 10^9
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
increase the power-of-10 exponent by the same number of units
10^-18

6. 0^5 =
exponent
10^-2
10^-18
0

7. Indicates the number to be multiplied.
base
2 x 10^9
3
Engineering notation

8. Valid powers of 10 for engineering notation are:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Same base
Because 4 multiplied by itself equals 16.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

9. A number with an exponent of 3 is often said to be
cubed
squared
10^-2
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. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
1
6.74 x 10^-7
itself

11. 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
0
cube-root key
same exponent
10^-1

12. To find the square root of any number - simply key in the number (the radicand) and press the
Calculator square-root key
10^-1
the radical sign with a little 3 that indicates the cube root:
you have to adjust the value of the exponent in order avoid changing the actual value.

13. Dividing by 10
Moving the decimal point to the left
increase the power-of-10 exponent by the same number of units
0
The solution exists - but not in the real number system.

14. A number with an exponent of 2 is often said to be
exponent
squared
Step 1. Divide the coefficients of the terms
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

15. Any number with an exponent of 1 is equal to
Same base
1 divided by that number with a positive exponent
exponent
itself

16. When you change the position of the decimal point in a coefficient value
Subtract the exponent
you have to adjust the value of the exponent in order avoid changing the actual value.
proper scientific
move the decimal point the same number of units to the right

17. 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
10^-18
same exponent
0
change both terms in order to keep the value the same.

18. To divide powers that have the same base:
the radical sign with a little 3 that indicates the cube root:
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
exponent

19. 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.
Scientific notation
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
cube root
itself

20. When you decrease the value of the power-of-10 exponent
negative number
0
rewrite one of the terms so that the exponents are equal
move the decimal point the same number of units to the right

21.
2 x 10^9
increase the power-of-10 exponent by the same number of units
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
Moving the decimal point to the left

22. To add powers of ten:
10^-2
you have to adjust the value of the exponent in order avoid changing the actual value.
move the decimal point the same number of units to the left
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

23. Numbers with exponents can be directly multiplied or divided only when they have the
Same base
Moving the decimal point to the left
Engineering 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.

24. Any number with a negative exponent is equal to
square root
same exponent
proper scientific
1 divided by that number with a positive exponent

25. Valid powers-of-10 for engineering notation
1. Multiply the coefficients 2. Add the exponents
cubed
must be multiples of 3 or 0
10^-1

26. The cube root of a negative number is also a
1. Divide the coefficients 2. Subtract the exponents
9 (3^2 = 9)
negative number
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

27. The decimal part
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
coefficient
decrease the power-of-10 exponent by the same number of units

28. For the 10
exponent
Engineering notation
10^-2
move the decimal point the same number of units to the left

29. A number - when multiplied by itself - is equal to a given number.
square root
5
When the exponent of a power-of-10 expression is a negative integer:
radical sign

30. Powers of ten can be added or subtracted only when their exponents
coefficient
Because 4 multiplied by itself equals 16.
Are Equal
0

31. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
10^1
Calculator square-root key
2
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

32. Any number with an exponent of 0 is equal to
itself
1
perfect square
0

33. The square root of zero is
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
square root
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

34. To multiply powers of 10:
cube-root key
radical sign
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.

35. The symbol for the cube root of a number 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
base
10^2
the radical sign with a little 3 that indicates the cube root:

36. The square root of 9 is
radical sign
3
1. Multiply the coefficients 2. Add the exponents
the radical sign with a little 3 that indicates the cube root:

37. 100 - or 1 with the decimal point moved two places to the right
same exponent
Are Equal
10^2
1 divided by that number with a positive exponent

38. To multiply or divide exponent terms that do not have the same base:
0
5
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
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.

39. The cube root of zero is
change both terms in order to keep the value the same.
Subtract the exponent
0
you have to adjust the value of the exponent in order avoid changing the actual value.

40. A very small number such as 0.000000674 can be written with scientific notation as
Not
6.74 x 10^-7
rewrite one of the terms so that the exponents are equal
Because 4 multiplied by itself equals 16.

41. A number is a second number which - when multiplied by itself three times - equals the original number.
squared
proper scientific
cube root
you have to adjust the value of the exponent in order avoid changing the actual value.

42. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
10^-2
a fractional decimal
cube-root key

43. When you move the decimal point in the coefficient to the left
0
rewrite one of the terms so that the exponents are equal
increase the power-of-10 exponent by the same number of units
Are Equal

44. 1 to any power is equal to
base
1
9 (3^2 = 9)
1. Divide the coefficients 2. Subtract the exponents

45. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Because 4 multiplied by itself equals 16.
Subtract the exponent
a fractional decimal
decrease the value of the exponent by 1 (dividing by 10)

46. To divide powers of ten:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
exponent
1
1. Divide the coefficients 2. Subtract the exponents

47. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Subtract the exponent
Are Equal
0

48. There are no special rules for adding and subtracting numbers that are written with exponents.
coefficient
Engineering notation
Moving the decimal point to the left
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

49. When you move the decimal point in the coefficient to the right
base
decrease the power-of-10 exponent by the same number of units
0
perfect square

50. The square of 3 is
1
10^1
cube root
9 (3^2 = 9)