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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. 10 - or 1 with the decimal point moved one place to the right
To multiply powers that have the same base:
10^-1
6.74 x 10^-7
10^1

2. A number with an exponent of 2 is often said to be
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
must be multiples of 3 or 0
When moving the decimal point to the left (dividing by 10)
squared

3. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
square root
you have to adjust the value of the exponent in order avoid changing the actual value.
1 divided by that number with a positive exponent

4. Valid powers of 10 for engineering notation are:
perfect square
6.74 x 10^-7
squared
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

5. 1 to any power is equal to
rewrite one of the terms so that the exponents are equal
0
1 divided by that number with a positive exponent
1

6. The square root of 9 is
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
9 (3^2 = 9)
3

7. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
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.
To multiply powers that have the same base:
coefficient

8. Dividing by 10
Moving the decimal point to the left
Moving the decimal point to the right
The solution exists - but not in the real number system.
coefficient

9. The decimal part
change both terms in order to keep the value the same.
adjust the value of the coefficient
a fractional decimal
coefficient

10. A very small number such as 0.000000674 can be written with scientific notation as
0
6.74 x 10^-7
change both terms in order to keep the value the same.
move the decimal point the same number of units to the left

11. Any number with a negative exponent is equal to
one digit to the left of the decimal point
1 divided by that number with a positive exponent
The solution exists - but not in the real number system.
1

12. Always 10 for scientific notation
base
1
10^-18
Because 4 multiplied by itself equals 16.

13. 1 to any power is equal to
When moving the decimal point to the left (dividing by 10)
coefficient
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1

14. 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
0
Same base
itself

15. 0^5 =
same exponent
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
decrease the value of the exponent by 1 (dividing by 10)

16. A number is a second number which - when multiplied by itself three times - equals the original number.
same exponent
perfect square
Engineering notation
cube root

17. The cube root of zero is
To multiply powers that have the same base:
2
0
one digit to the left of the decimal point

18. To find the square root of any number - simply key in the number (the radicand) and press the
square root
Are Equal
Calculator square-root key
0

19. Any number with an exponent of 1 is equal to
change both terms in order to keep the value the same.
move the decimal point the same number of units to the right
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
itself

20. Indicates the number to be multiplied.
1
change both terms in order to keep the value the same.
To multiply powers that have the same base:
base

21. Negative cube roots are okay ... negative square roots are
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.
To multiply powers that have the same base:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Not

22. A number with an exponent of 3 is often said to be
cubed
cube root
decrease the value of the exponent by 1 (dividing by 10)
1. Divide the coefficients 2. Subtract the exponents

23. 1^4 =
decrease the value of the exponent by 1 (dividing by 10)
1
itself
Subtract the exponent

24. To subtract powers of ten:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-18
Are Equal
6.74 x 10^-7

25. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
1
increase the power-of-10 exponent by the same number of units
must be multiples of 3 or 0

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
1. Divide the coefficients 2. Subtract the exponents
cube-root key
Moving the decimal point to the left
itself

27. 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
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the right
1 divided by that number with a positive exponent

28. Any number with an exponent of 0 is equal to
1. Divide the coefficients 2. Subtract the exponents
1
The solution exists - but not in the real number system.
1. Multiply the coefficients 2. Add the exponents

29. The symbol for the cube root of a number is
Are Equal
the radical sign with a little 3 that indicates the cube 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
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.

30. 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
10^-1
change both terms in order to keep the value the same.
Moving the decimal point to the left
0

31. 0 to any power is equal to
10^2
0
9 (3^2 = 9)
2

32. When you increase the value of the power-of-10 exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the left
move the decimal point the same number of units to the right
base

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

34. Represents 1 preceded by 17 zeros and a decimal point.
Step 1. Divide the coefficients of the terms
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-18
a fractional decimal

35. Increase the value of the exponent by 1 (multiplying by 10)
1. Multiply the coefficients 2. Add the exponents
When moving the decimal point to the left (dividing by 10)
itself
1

36. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
6.74 x 10^-7
1. Divide the coefficients 2. Subtract the exponents
2

37. To multiply or divide exponent terms that do not have the same base:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-2
When the exponent of a power-of-10 expression is a negative integer:
coefficient

38. When you change the position of the decimal point in a coefficient value
0
you have to adjust the value of the exponent in order avoid changing the actual value.
10^-18
Same base

39. To divide powers of 10:
Calculator square-root key
decrease the value of the exponent by 1 (dividing by 10)
Step 1. Divide the coefficients of the terms
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

40. Don't bother trying to find the square root of a negative number.
10^1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
The solution exists - but not in the real number system.
When moving the decimal point to the left (dividing by 10)

41. For the 10
1 divided by that number with a positive exponent
When moving the decimal point to the left (dividing by 10)
exponent
0

42. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
increase the power-of-10 exponent by the same number of units
decrease the power-of-10 exponent by the same number of units
radical sign

43. The square root of zero is
0
Engineering notation
1
The solution exists - but not in the real number system.

44. Multiplying by 10
The solution exists - but not in the real number system.
Are Equal
Moving the decimal point to the right
Scientific notation

45. A number - when multiplied by itself - is equal to a given number.
squared
6.74 x 10^-7
square root
10^1

46. When you decrease the value of the power-of-10 exponent
Are Equal
square root
2
move the decimal point the same number of units to the right

47. Powers of ten can be added or subtracted only when their exponents
Step 1. Divide the coefficients of the terms
Are Equal
adjust the value of the coefficient
Because 4 multiplied by itself equals 16.

48. The square of 3 is
9 (3^2 = 9)
cube root
Subtract the exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

49. 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
10^1
adjust the value of the coefficient
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
2 x 10^9

50. To multiply powers of ten:
decrease the value of the exponent by 1 (dividing by 10)
1. Multiply the coefficients 2. Add the exponents
Moving the decimal point to the left
Engineering notation