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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 divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
increase the power-of-10 exponent by the same number of units
2 x 10^9
Step 1. Divide the coefficients of the terms
Subtract the exponent

2. Scientific notation requires there to be only
the radical sign with a little 3 that indicates the cube root:
3
coefficient
one digit to the left of the decimal point

3. The cube root of zero is
0
1. Multiply the coefficients 2. Add the exponents
one digit to the left of the decimal point
Moving the decimal point to the right

4. Always 10 for scientific notation
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^1
1
base

5. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
adjust the value of the coefficient
exponent
decrease the power-of-10 exponent by the same number of units

6. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Step 1. Divide the coefficients of the terms
increase the power-of-10 exponent by the same number of units
When moving the decimal point to the left (dividing by 10)

7. 0 to any power is equal to
1
Moving the decimal point to the right
base
0

8. A negative exponent does not mean the decimal value is negative. It means the decimal value is
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
a fractional decimal
Moving the decimal point to the right
decrease the power-of-10 exponent by the same number of units

9. Numbers with exponents can be directly multiplied or divided only when they have the
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
Because 4 multiplied by itself equals 16.
exponent
Same base

10. For the 10
exponent
Subtract the exponent
cube root
proper scientific

11. What number multiplied by itself is equal to 16? The answer is 4. Why?
squared
Because 4 multiplied by itself equals 16.
2
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

12. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
10^-1
coefficient
Not

13. 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
square root
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
10^2
2

14.
To multiply powers that have the same 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
increase the power-of-10 exponent by the same number of units
10^1

15. To divide powers of 10:
2 x 10^9
10^-1
Step 1. Divide the coefficients of the terms
one digit to the left of the decimal point

16. The square root of 9 is
cubed
3
1
same exponent

17. To add powers of ten:
5
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
negative number
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

18. A number with an exponent of 3 is often said to be
decrease the value of the exponent by 1 (dividing by 10)
cube-root key
1
cubed

19. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
decrease the power-of-10 exponent by the same number of units
Because 4 multiplied by itself equals 16.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

20. When you decrease the value of the power-of-10 exponent
2
9 (3^2 = 9)
move the decimal point the same number of units to the right
10^-1

21. 1^4 =
10^2
Because 4 multiplied by itself equals 16.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1

22. Indicates the number to be multiplied.
3
rewrite one of the terms so that the exponents are equal
base
increase the power-of-10 exponent by the same number of units

23. The decimal part
0
1. Divide the coefficients 2. Subtract the exponents
exponent
coefficient

24. 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
cube root
change both terms in order to keep the value the same.
Same base
When the exponent of a power-of-10 expression is a negative integer:

25. 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. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
cube-root key
move the decimal point the same number of units to the right

26. 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
10^1
decrease the value of the exponent by 1 (dividing by 10)
cube-root key
6.74 x 10^-7

27. To find the square root of any number - simply key in the number (the radicand) and press the
5
1. Divide the coefficients 2. Subtract the exponents
Calculator square-root key
0

28. Don't bother trying to find the square root of a negative number.
2
The solution exists - but not in the real number system.
1
move the decimal point the same number of units to the right

29. There are no special rules for adding and subtracting numbers that are written with exponents.
squared
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
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. 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.
move the decimal point the same number of units to the left
proper scientific
adjust the value of the coefficient
When the exponent of a power-of-10 expression is a negative integer:

31. Step 1: Add the exponents Step 2: Use the common base
10^-1
1. Multiply the coefficients 2. Add the exponents
To multiply powers that have the same base:
cube root

32. 1 to any power is equal to
When the exponent of a power-of-10 expression is a negative integer:
9 (3^2 = 9)
rewrite one of the terms so that the exponents are equal
1

33. 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.
1
cube-root key
1
Scientific notation

34. When you change the position of the decimal point in a coefficient value
10^-18
perfect square
proper scientific
you have to adjust the value of the exponent in order avoid changing the actual value.

35. When you move the decimal point in the coefficient to the left
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.
10^1
10^2
increase the power-of-10 exponent by the same number of units

36. 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
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
perfect square
0

37. 100 - or 1 with the decimal point moved two places to the right
Same base
0
10^2
Subtract the exponent

38. Multiplying by 10
To multiply powers that have the same base:
Moving the decimal point to the right
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
you have to adjust the value of the exponent in order avoid changing the actual value.

39. 5^1 =
5
negative number
When moving the decimal point to the left (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

40. Increase the value of the exponent by 1 (multiplying by 10)
cube-root key
When moving the decimal point to the left (dividing by 10)
1
1. Divide the coefficients 2. Subtract the exponents

41. Any number with an exponent of 0 is equal to
1
Subtract the exponent
Because 4 multiplied by itself equals 16.
0

42. 3^0 =
Moving the decimal point to the left
1
Because 4 multiplied by itself equals 16.
decrease the power-of-10 exponent by the same number of units

43. Powers of ten can be added or subtracted only when their exponents
10^2
Are Equal
negative number
When the exponent of a power-of-10 expression is a negative integer:

44. Negative cube roots are okay ... negative square roots are
To multiply powers that have the same base:
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Not

45. When you move the decimal point in the coefficient to the right
To multiply powers that have the same base:
decrease the power-of-10 exponent by the same number of units
exponent
Moving the decimal point to the left

46. The square root of zero is
0
cube root
base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

47. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
a fractional decimal
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
increase the power-of-10 exponent by the same number of units

48. A number - when multiplied by itself - is equal to a given number.
the radical sign with a little 3 that indicates the cube root:
square root
6.74 x 10^-7
Scientific notation

49. = 0.1 - or 1 with the decimal point moved one place to the left.
move the decimal point the same number of units to the left
base
Scientific notation
10^-1

50. To multiply or divide exponent terms that do not have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
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