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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. 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
rewrite one of the terms so that the exponents are equal
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
adjust the value of the coefficient

2. A number - when multiplied by itself - is equal to a given number.
Because 4 multiplied by itself equals 16.
squared
Step 1. Divide the coefficients of the terms
square root

3. 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.
base
radical sign
decrease the power-of-10 exponent by the same number of units
increase the power-of-10 exponent by the same number of units

4. 0 to any power is equal to
Because 4 multiplied by itself equals 16.
0
Calculator square-root key
squared

5. 10 - or 1 with the decimal point moved one place to the right
rewrite one of the terms so that the exponents are equal
10^1
increase the power-of-10 exponent by the same number of units
5

6. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
rewrite one of the terms so that the exponents are equal
proper scientific
square root
must be multiples of 3 or 0

7. The square of 3 is
9 (3^2 = 9)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Step 1. Divide the coefficients of the terms

8. 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
base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
same exponent

9. 5^1 =
decrease the power-of-10 exponent by the same number of units
10^2
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.
5

10. 1^4 =
1
cubed
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left

11. The cube root of a negative number is also a
negative number
5
When the exponent of a power-of-10 expression is a negative integer:
cube-root key

12. 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
2
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Moving the decimal point to the right

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
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
move the decimal point the same number of units to the left
The solution exists - but not in the real number system.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

14.
decrease the value of the exponent by 1 (dividing by 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
cubed

15. The square root of 9 is
3
squared
10^2
10^-2

16. The symbol for the cube root of a number is
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
the radical sign with a little 3 that indicates the cube root:
When the exponent of a power-of-10 expression is a negative integer:
move the decimal point the same number of units to the left

17. Always 10 for scientific notation
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

18. Numbers with exponents can be directly multiplied or divided only when they have the
negative number
Same base
1
2 x 10^9

19. 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
Moving the decimal point to the left
0
Because 4 multiplied by itself equals 16.
cube-root key

20. 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.
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Engineering notation
1 divided by that number with a positive exponent

21. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Because 4 multiplied by itself equals 16.
squared
a fractional decimal
9 (3^2 = 9)

22. To add powers of ten:
10^2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
proper scientific
0

23. The decimal part
coefficient
exponent
Are Equal
Calculator square-root key

24. To divide powers of 10:
cube root
Moving the decimal point to the left
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Step 1. Divide the coefficients of the terms

25. Represents 1 preceded by 17 zeros and a decimal point.
change both terms in order to keep the value the same.
base
10^-18
Are Equal

26. 3^0 =
base
decrease the value of the exponent by 1 (dividing by 10)
decrease the power-of-10 exponent by the same number of units
1

27. Multiplying by 10
When the exponent of a power-of-10 expression is a negative integer:
Moving the decimal point to the right
1 divided by that number with a positive exponent
1

28. Negative cube roots are okay ... negative square roots are
rewrite one of the terms so that the exponents are equal
cube-root key
base
Not

29. 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^-1
When the exponent of a power-of-10 expression is a negative integer:
a fractional decimal

30. Indicates the number of times the base is to be multiplied.
The solution exists - but not in the real number system.
6.74 x 10^-7
10^-2
exponent

31. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
10^2
10^1
square root

32. A number with an exponent of 2 is often said to be
0
squared
1
cubed

33. For the 10
exponent
10^-18
perfect square
same exponent

34. 1 to any power is equal to
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
adjust the value of the coefficient
perfect square
1

35. A very small number such as 0.000000674 can be written with scientific notation as
cubed
10^2
When moving the decimal point to the left (dividing by 10)
6.74 x 10^-7

36. When you change the position of the decimal point in a coefficient value
perfect square
decrease the power-of-10 exponent by the same number of units
you have to adjust the value of the exponent in order avoid changing the actual value.
Scientific notation

37. Any number with a negative exponent is equal to
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
a fractional decimal
1 divided by that number with a positive exponent

38. 100 - or 1 with the decimal point moved two places to the right
10^2
0
When the exponent of a power-of-10 expression is a negative integer:
coefficient

39. Any number with an exponent of 1 is equal to
itself
must be multiples of 3 or 0
Because 4 multiplied by itself equals 16.
move the decimal point the same number of units to the right

40. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Because 4 multiplied by itself equals 16.
must be multiples of 3 or 0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

41. To add or subtract numbers written with exponents:
base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Engineering notation
exponent

42. Step 1: Add the exponents Step 2: Use the common base
1. Divide the coefficients 2. Subtract the exponents
2
Moving the decimal point to the right
To multiply powers that have the same base:

43. To multiply or divide exponent terms that do not have the same base:
6.74 x 10^-7
move the decimal point the same number of units to the right
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
itself

44. Indicates the number to be multiplied.
9 (3^2 = 9)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
base
Same base

45. A number is a second number which - when multiplied by itself three times - equals the original number.
0
move the decimal point the same number of units to the right
3
cube root

46. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
10^-1
The solution exists - but not in the real number system.
5

47. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
a fractional decimal
decrease the value of the exponent by 1 (dividing by 10)
9 (3^2 = 9)
2 x 10^9

48. 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. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
perfect square
same exponent
1

49. When you increase the value of the power-of-10 exponent
Because 4 multiplied by itself equals 16.
move the decimal point the same number of units to the left
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
To multiply powers that have the same base:

50. To divide powers of ten:
one digit to the left of the decimal point
1. Divide the coefficients 2. Subtract the exponents
0
rewrite one of the terms so that the exponents are equal