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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. = 0.01 - or 1 with the decimal point moved two places to the left.
exponent
3
10^-2
a fractional decimal

2. A number with an exponent of 2 is often said to be
When moving the decimal point to the left (dividing by 10)
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
squared
Not

3. 1^4 =
increase the power-of-10 exponent by the same number of units
1
2 x 10^9
Calculator square-root key

4. 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
Step 1. Divide the coefficients of the terms
same exponent
decrease the power-of-10 exponent by the same number of units
Engineering notation

5. 1 to any power is equal to
The solution exists - but not in the real number system.
6.74 x 10^-7
itself
1

6. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
decrease the value of the exponent by 1 (dividing by 10)
perfect square
When the exponent of a power-of-10 expression is a negative integer:

7. Numbers with exponents can be directly multiplied or divided only when they have the
1
Same base
negative number
proper scientific

8. Step 1: Add the exponents Step 2: Use the common base
a fractional decimal
2
10^-18
To multiply powers that have the same base:

9. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
When the exponent of a power-of-10 expression is a negative integer:
1
negative number

10. To divide powers of 10:
Step 1. Divide the coefficients of the terms
9 (3^2 = 9)
10^2
Scientific notation

11. = 0.1 - or 1 with the decimal point moved one place to the left.
cubed
10^-1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
same exponent

12. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
1. Multiply the coefficients 2. Add the exponents
increase the power-of-10 exponent by the same number of units
Subtract the exponent
squared

13. The square root of 9 is
6.74 x 10^-7
5
3
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.

14. When you move the decimal point in the coefficient to the right
Engineering notation
Because 4 multiplied by itself equals 16.
decrease the power-of-10 exponent by the same number of units
10^2

15. 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
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.
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
When moving the decimal point to the left (dividing by 10)
decrease the value of the exponent by 1 (dividing by 10)

16. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Same base
proper scientific
1

17. The cube root of zero is
0
square root
coefficient
squared

18. The cube root of a negative number is also a
Subtract the exponent
negative number
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

19. To divide powers that have the same base:
Moving the decimal point to the right
decrease the power-of-10 exponent by the same number of units
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^2

20. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
When the exponent of a power-of-10 expression is a negative integer:
2
move the decimal point the same number of units to the left

21.
Are Equal
move the decimal point the same number of units to the right
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
exponent

22. When you decrease the value of the power-of-10 exponent
same exponent
move the decimal point the same number of units to the right
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. Multiply the coefficients 2. Add the exponents

23. Valid powers of 10 for engineering notation are:
Not
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
Are Equal
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

24. A number - when multiplied by itself - is equal to a given number.
square root
the radical sign with a little 3 that indicates the cube root:
1
radical sign

25. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
2
coefficient

26. The symbol for the cube root of a number is
exponent
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.
Moving the decimal point to the left
the radical sign with a little 3 that indicates the cube root:

27. Any number with an exponent of 1 is equal to
itself
perfect square
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
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

28. 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
exponent
Engineering notation
10^1

29. Multiplying by 10
Moving the decimal point to the right
increase the power-of-10 exponent by the same number of units
1. Divide the coefficients 2. Subtract the exponents
Subtract the exponent

30. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
Moving the decimal point to the right
Not
5

31. Any number with an exponent of 0 is equal to
1
exponent
proper scientific
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. 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.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
perfect square
10^1

33. There are no special rules for adding and subtracting numbers that are written with exponents.
2
move the decimal point the same number of units to the right
To multiply powers that have the same base:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

34. The square of 3 is
10^-18
9 (3^2 = 9)
Moving the decimal point to the right
one digit to the left of the decimal point

35. Scientific notation requires there to be only
cube root
you have to adjust the value of the exponent in order avoid changing the actual value.
1
one digit to the left of the decimal point

36. Increase the value of the exponent by 1 (multiplying by 10)
2 x 10^9
squared
9 (3^2 = 9)
When moving the decimal point to the left (dividing by 10)

37. A number with an exponent of 3 is often said to be
0
cubed
Moving the decimal point to the left
Because 4 multiplied by itself equals 16.

38. To multiply powers of ten:
5
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1. Multiply the coefficients 2. Add the exponents
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

39. 5^1 =
5
Moving the decimal point to the left
same exponent
increase the power-of-10 exponent by the same number of units

40. 100 - or 1 with the decimal point moved two places to the right
exponent
same exponent
exponent
10^2

41. To subtract powers of ten:
Are Equal
decrease the value of the exponent by 1 (dividing by 10)
cube-root key
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

42. Indicates the number of times the base is to be multiplied.
exponent
3
decrease the power-of-10 exponent by the same number of units
negative number

43. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
When the exponent of a power-of-10 expression is a negative integer:
square root
To multiply powers that have the same base:

44. Don't bother trying to find the square root of a negative number.
9 (3^2 = 9)
The solution exists - but not in the real number system.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
rewrite one of the terms so that the exponents are equal

45. Represents 1 preceded by 17 zeros and a decimal point.
proper scientific
10^-1
10^-18
the radical sign with a little 3 that indicates the cube root:

46. 1 to any power is equal to
square root
0
1
cube-root key

47. The square root of zero is
radical sign
0
Subtract the exponent
1. Multiply the coefficients 2. Add the exponents

48. Valid powers-of-10 for engineering notation
0
must be multiples of 3 or 0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
When the exponent of a power-of-10 expression is a negative integer:

49. 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 right
you have to adjust the value of the exponent in order avoid changing the actual value.
negative number

50. When the exponents are not the same
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
0
0
rewrite one of the terms so that the exponents are equal