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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. Dividing by 10
squared
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
increase the power-of-10 exponent by the same number of units
Moving the decimal point to the left

2. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1. Multiply the coefficients 2. Add the exponents
2 x 10^9

3. Don't bother trying to find the square root of a negative number.
10^-18
a fractional decimal
The solution exists - but not in the real number system.
itself

4. 1 to any power is equal to
10^1
square root
Same base
1

5. Multiplying by 10
Step 1. Divide the coefficients of the terms
Moving the decimal point to the right
Engineering notation
To multiply powers that have the same base:

6. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Engineering notation
you have to adjust the value of the exponent in order avoid changing the actual value.
change both terms in order to keep the value the same.

7. The cube root of a negative number is also a
negative number
cube root
squared
exponent

8. Indicates the number to be multiplied.
exponent
base
cube-root key
10^1

9. To divide powers of ten:
3
1. Divide the coefficients 2. Subtract the exponents
1
When the exponent of a power-of-10 expression is a negative integer:

10. Indicates the number of times the base is to be multiplied.
Engineering notation
1
increase the power-of-10 exponent by the same number of units
exponent

11. 0 to any power is equal to
0
Not
perfect square
When moving the decimal point to the left (dividing by 10)

12. Any number with an exponent of 0 is equal to
1
itself
When moving the decimal point to the left (dividing by 10)
cube-root key

13. Any number with an exponent of 1 is equal to
cubed
itself
proper scientific
exponent

14. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
1
increase the power-of-10 exponent by the same number of units
adjust the value of the coefficient

15. To subtract powers of ten:
Same base
Step 1. Divide the coefficients of the terms
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

16. To divide powers of 10:
increase the power-of-10 exponent by the same number of units
Step 1. Divide the coefficients of the terms
cube root
itself

17. = 0.1 - or 1 with the decimal point moved one place to the left.
same exponent
9 (3^2 = 9)
10^-1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

18. 3^0 =
Are Equal
square root
1
10^-18

19. A number with an exponent of 3 is often said to be
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
When the exponent of a power-of-10 expression is a negative integer:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
cubed

20. Any number with a negative exponent is equal to
0
3
Moving the decimal point to the right
1 divided by that number with a positive exponent

21. Scientific notation requires there to be only
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
one digit to the left of the decimal point
10^-1

22. A number with an exponent of 2 is often said to be
10^2
increase the power-of-10 exponent by the same number of units
10^-2
squared

23. Powers of ten can be added or subtracted only when their exponents
Are Equal
5
Subtract the exponent
To multiply powers that have the same base:

24. A negative exponent does not mean the decimal value is negative. It means the decimal value is
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
a fractional decimal
Same base

25. 1 to any power is equal to
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
adjust the value of the coefficient
1
decrease the power-of-10 exponent by the same number of units

26. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
10^-2
1
1. Divide the coefficients 2. Subtract the exponents

27. When you change the position of the decimal point in a coefficient value
you have to adjust the value of the exponent in order avoid changing the actual value.
negative number
Scientific notation
cube-root key

28. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
the radical sign with a little 3 that indicates the cube root:

29. A very small number such as 0.000000674 can be written with scientific notation as
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Not
a fractional decimal
6.74 x 10^-7

30. Increase the value of the exponent by 1 (multiplying by 10)
cube-root key
Engineering notation
When moving the decimal point to the left (dividing by 10)
exponent

31. For the 10
The solution exists - but not in the real number system.
decrease the value of the exponent by 1 (dividing by 10)
0
exponent

32. 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.
must be multiples of 3 or 0
When the exponent of a power-of-10 expression is a negative integer:
Subtract the exponent
squared

33. 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 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
6.74 x 10^-7
cube root
10^-1

34. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
same exponent
exponent
1

35. The square root of 9 is
10^1
the radical sign with a little 3 that indicates the cube root:
3
1

36. The square of 3 is
2
exponent
1. Divide the coefficients 2. Subtract the exponents
9 (3^2 = 9)

37. 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.
cubed
a fractional decimal
same exponent

38. To find the square root of any number - simply key in the number (the radicand) and press the
one digit to the left of the decimal point
0
Calculator square-root key
Are Equal

39. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
you have to adjust the value of the exponent in order avoid changing the actual value.
0
Moving the decimal point to the right

40.
Scientific 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
one digit to the left of the decimal point
Engineering notation

41. The cube root of zero is
0
When moving the decimal point to the left (dividing by 10)
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^-1

42. 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.
Engineering notation
10^1
increase the power-of-10 exponent by the same number of units
perfect square

43. 10 - or 1 with the decimal point moved one place to the right
When moving the decimal point to the left (dividing by 10)
10^1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
2

44. To multiply powers of ten:
Moving the decimal point to the right
1
1. Multiply the coefficients 2. Add the exponents
Step 1. Divide the coefficients of the terms

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
move the decimal point the same number of units to the left
cube-root key
When moving the decimal point to the left (dividing by 10)
the radical sign with a little 3 that indicates the cube root:

46. What number multiplied by itself is equal to 16? The answer is 4. Why?
decrease the power-of-10 exponent by the same number of units
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
Because 4 multiplied by itself equals 16.

47. 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
rewrite one of the terms so that the exponents are equal
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
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

48. 100 - or 1 with the decimal point moved two places to the right
To multiply powers that have the same base:
decrease the power-of-10 exponent by the same number of units
10^2
increase the power-of-10 exponent by the same number of units

49. Is a special form of power-of-10 notation where the exponents for the 10s must be 0 or multiples of 3. There must be 1 - 2 - or 3 digits on the left side of the decimal point.
Engineering notation
base
Moving the decimal point to the right
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

50. 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.
radical sign
base
10^2
Not