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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. Adding and subtracting powers of ten can be a bit more complicated than multiplying and dividing. The main problem is that powers of ten can be added or subtracted only when both terms have the
same exponent
a fractional decimal
Moving the decimal point to the left
1

2. To multiply powers of ten:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
increase the power-of-10 exponent by the same number of units
1. Multiply the coefficients 2. Add the exponents
exponent

3. 0^5 =
adjust the value of the coefficient
decrease the power-of-10 exponent by the same number of units
must be multiples of 3 or 0
0

4. 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
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
a fractional decimal
1 divided by that number with a positive exponent
change both terms in order to keep the value the same.

5. To multiply or divide exponent terms that do not have the same base:
coefficient
10^-18
adjust the value of the coefficient
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

6. 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
5
Scientific notation
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
adjust the value of the coefficient

7. Any number with an exponent of 0 is equal to
1
exponent
10^-2
0

8. 1 to any power is equal to
base
cube root
1. Multiply the coefficients 2. Add the exponents
1

9. There are no special rules for adding and subtracting numbers that are written with exponents.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
proper scientific
coefficient
3

10. Any number with an exponent of 1 is equal to
Because 4 multiplied by itself equals 16.
one digit to the left of the decimal point
you have to adjust the value of the exponent in order avoid changing the actual value.
itself

11. The cube root of a negative number is also a
negative number
rewrite one of the terms so that the exponents are equal
0
Moving the decimal point to the right

12. 10 - or 1 with the decimal point moved one place to the right
1
adjust the value of the coefficient
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
10^1

13. The square root of 9 is
Same base
1. Divide the coefficients 2. Subtract the exponents
3
2 x 10^9

14. 0 to any power is equal to
1
coefficient
5
0

15.
The solution exists - but not in the real number system.
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
radical sign
move the decimal point the same number of units to the left

16. To divide powers of ten:
cube-root key
Subtract the exponent
1. Divide the coefficients 2. Subtract the exponents
2

17. 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.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
perfect square
Not
proper scientific

18. Dividing by 10
Not
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

19. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
0
To multiply powers that have the same base:
same exponent

20. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
exponent
move the decimal point the same number of units to the left
To multiply powers that have the same base:
2 x 10^9

21. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
decrease the power-of-10 exponent by the same number of units
6.74 x 10^-7
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

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

23. 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
1. Multiply the coefficients 2. Add the exponents
move the decimal point the same number of units to the left
6.74 x 10^-7

24. The symbol for the cube root of a number is
1
1
2 x 10^9
the radical sign with a little 3 that indicates the cube root:

25. Always 10 for scientific notation
cube-root key
base
Engineering notation
1

26. Step 1: Add the exponents Step 2: Use the common base
the radical sign with a little 3 that indicates the cube root:
To multiply powers that have the same base:
5
3

27. When you decrease the value of the power-of-10 exponent
change both terms in order to keep the value the same.
move the decimal point the same number of units to the right
rewrite one of the terms so that the exponents are equal
must be multiples of 3 or 0

28. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left
negative number
cube-root key

29. 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
2 x 10^9
10^-2

30. Negative cube roots are okay ... negative square roots are
Not
1. Divide the coefficients 2. Subtract the exponents
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
Engineering notation

31. To multiply powers of 10:
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.
3
decrease the value of the exponent by 1 (dividing by 10)
Calculator square-root key

32. Valid powers-of-10 for engineering notation
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
must be multiples of 3 or 0
Step 1. Divide the coefficients of the terms
10^-1

33. = 0.1 - or 1 with the decimal point moved one place to the left.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-1
squared

34. A negative exponent does not mean the decimal value is negative. It means the decimal value is
decrease the power-of-10 exponent by the same number of units
a fractional decimal
Engineering notation
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

35. Increase the value of the exponent by 1 (multiplying by 10)
1
When moving the decimal point to the left (dividing by 10)
adjust the value of the coefficient
cube root

36. Powers of ten can be added or subtracted only when their exponents
0
Are Equal
Subtract the exponent
Because 4 multiplied by itself equals 16.

37. 100 - or 1 with the decimal point moved two places to the right
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
one digit to the left of the decimal point
10^2
1. Multiply the coefficients 2. Add the exponents

38. 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.
exponent
0
radical sign
move the decimal point the same number of units to the left

39. When you increase the value of the power-of-10 exponent
1
0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
move the decimal point the same number of units to the left

40. For the 10
1
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.
exponent

41. To divide powers that have the same base:
Scientific notation
coefficient
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
radical sign

42. The square of 3 is
decrease the power-of-10 exponent by the same number of units
0
1. Divide the coefficients 2. Subtract the exponents
9 (3^2 = 9)

43. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
the radical sign with a little 3 that indicates the cube root:
Subtract the exponent
10^-2

44. Indicates the number of times the base is to be multiplied.
Engineering notation
you have to adjust the value of the exponent in order avoid changing the actual value.
exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

45. 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.
Engineering notation
1
move the decimal point the same number of units to the left
Scientific notation

46. Any number with a negative exponent is equal to
proper scientific
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1 divided by that number with a positive exponent
exponent

47. When moving the decimal point to the right (multiplying by 10)
The solution exists - but not in the real number system.
decrease the value of the exponent by 1 (dividing by 10)
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
rewrite one of the terms so that the exponents are equal

48. To divide powers of 10:
2
exponent
decrease the power-of-10 exponent by the same number of units
Step 1. Divide the coefficients of the terms

49. A number - when multiplied by itself - is equal to a given number.
To multiply powers that have the same base:
move the decimal point the same number of units to the right
square root
negative number

50. 5^1 =
To multiply powers that have the same base:
decrease the value of the exponent by 1 (dividing by 10)
5
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