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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. To add powers of ten:
Calculator square-root key
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
itself
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

2. 3^0 =
2 x 10^9
10^2
1
same exponent

3. Represents 1 preceded by 17 zeros and a decimal point.
cube-root key
3
itself
10^-18

4. Increase the value of the exponent by 1 (multiplying by 10)
must be multiples of 3 or 0
When moving the decimal point to the left (dividing by 10)
0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

5. Multiplying by 10
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Moving the decimal point to the right
coefficient
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

6. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
cube-root key
10^-1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

7. To subtract 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
Same base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^2

8. The square root of 9 is
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
3
radical sign
move the decimal point the same number of units to the left

9. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
3
perfect square

10. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
Because 4 multiplied by itself equals 16.
Calculator square-root key
2
Subtract the exponent

11. What number multiplied by itself is equal to 16? The answer is 4. Why?
coefficient
Because 4 multiplied by itself equals 16.
one digit to the left of the decimal point
the radical sign with a little 3 that indicates the cube root:

12. The cube root of a negative number is also a
3
rewrite one of the terms so that the exponents are equal
2
negative number

13. 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.
1
perfect square
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
itself

14. When you change the position of the decimal point in a coefficient value
10^-2
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
1. Divide the coefficients 2. Subtract the exponents

15. 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.
To multiply powers that have the same base:
decrease the power-of-10 exponent by the same number of units
Scientific notation
base

16. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
cube root
0
exponent

17. The square of 3 is
9 (3^2 = 9)
Moving the decimal point to the left
2 x 10^9
10^2

18. 10^-1 = 0.1 - or 1 with the decimal point moved one place to the left. 10^-2 = 0.01 - or 1 with the decimal point moved two places to the left. 10^-18 represents 1 preceded by 17 zeros and a decimal point.
1
When the exponent of a power-of-10 expression is a negative integer:
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

19. When you move the decimal point in the coefficient to the right
Scientific notation
change both terms in order to keep the value the same.
decrease the power-of-10 exponent by the same number of units
Not

20. Any number with an exponent of 0 is equal to
1
a fractional decimal
exponent
To multiply powers that have the same base:

21. 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
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
Because 4 multiplied by itself equals 16.
0

22. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
3
0
10^2

23. A number with an exponent of 3 is often said to be
To multiply powers that have the same base:
5
cubed
coefficient

24. A number - when multiplied by itself - is equal to a given number.
9 (3^2 = 9)
square root
3
0

25. Dividing by 10
Moving the decimal point to the right
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Moving the decimal point to the left

26. The cube root of zero is
Step 1. Divide the coefficients of the terms
10^-18
The solution exists - but not in the real number system.
0

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

28. When you increase the value of the power-of-10 exponent
10^-2
When moving the decimal point to the left (dividing by 10)
move the decimal point the same number of units to the left
cubed

29. 5^1 =
10^2
5
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

30. 0^5 =
10^1
0
proper scientific
3

31. Numbers with exponents can be directly multiplied or divided only when they have the
rewrite one of the terms so that the exponents are equal
Same base
increase the power-of-10 exponent by the same number of units
radical sign

32. Indicates the number of times the base is to be multiplied.
increase the power-of-10 exponent by the same number of units
square root
exponent
1. Multiply the coefficients 2. Add the exponents

33. 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.
0
1 divided by that number with a positive exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
radical sign

34. Valid powers of 10 for engineering notation are:
Scientific notation
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

35. To divide powers that have the same base:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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
rewrite one of the terms so that the exponents are equal
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

36. The decimal part
coefficient
1
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

37. Indicates the number to be multiplied.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
base
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
6.74 x 10^-7

38. For the 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
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
exponent
same exponent

39. To multiply powers of 10:
decrease the power-of-10 exponent by the same number of units
increase the power-of-10 exponent by the same number of units
coefficient
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.

40. When you decrease the value of the power-of-10 exponent
10^-1
10^2
Scientific notation
move the decimal point the same number of units to the right

41. Step 1: Add the exponents Step 2: Use the common base
decrease the value of the exponent by 1 (dividing by 10)
1 divided by that number with a positive exponent
To multiply powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

42. 1 to any power is equal to
negative number
1
square root
exponent

43. When the exponents are not the same
you have to adjust the value of the exponent in order avoid changing the actual value.
radical sign
rewrite one of the terms so that the exponents are equal
When moving the decimal point to the left (dividing by 10)

44. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
negative number
Because 4 multiplied by itself equals 16.
cubed

45. 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
Engineering notation
10^1
cube-root key
Not

46. To divide powers of 10:
cube root
Step 1. Divide the coefficients of the terms
Calculator square-root key
1

47. Powers of ten can be added or subtracted only when their exponents
0
Are Equal
base
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

48. The square root of zero is
negative number
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
2 x 10^9
0

49. Always 10 for scientific notation
base
square root
10^2
2 x 10^9

50. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
base
2
Calculator square-root key