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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. Indicates the number of times the base is to be multiplied.
decrease the power-of-10 exponent by the same number of units
When the exponent of a power-of-10 expression is a negative integer:
exponent
2

2. A number with an exponent of 2 is often said to be
Subtract the exponent
perfect square
squared
exponent

3. 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
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1. Multiply the coefficients 2. Add the exponents

4. Valid powers of 10 for engineering notation are:
adjust the value of the coefficient
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1

5. To divide powers of ten:
increase the power-of-10 exponent by the same number of units
Engineering notation
itself
1. Divide the coefficients 2. Subtract the exponents

6. The cube root of a negative number is also a
cube root
negative number
adjust the value of the coefficient
Same base

7. 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
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
decrease the value of the exponent by 1 (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

8. A number is a second number which - when multiplied by itself three times - equals the original number.
radical sign
cube root
2 x 10^9
Engineering notation

9. 0^5 =
0
perfect square
Moving the decimal point to the left
coefficient

10. 3^0 =
itself
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
3

11. A number with an exponent of 3 is often said to be
10^-18
Step 1. Divide the coefficients of the terms
cubed
adjust the value of the coefficient

12. 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.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Engineering notation
10^-18
a fractional decimal

13. Numbers with exponents can be directly multiplied or divided only when they have the
When moving the decimal point to the left (dividing by 10)
increase the power-of-10 exponent by the same number of units
Same base
adjust the value of the coefficient

14. Don't bother trying to find the square root of a negative number.
1. Multiply the coefficients 2. Add the exponents
1 divided by that number with a positive exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
The solution exists - but not in the real number system.

15. Dividing by 10
Same base
Moving the decimal point to the left
decrease the power-of-10 exponent by the same number of units
squared

16. Always 10 for scientific notation
cube root
proper scientific
1
base

17. 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
10^-2
cube-root key
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

18. Multiplying by 10
1. Multiply the coefficients 2. Add the exponents
exponent
1
Moving the decimal point to the right

19. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
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
2
must be multiples of 3 or 0

20. 1 to any power is equal to
6.74 x 10^-7
adjust the value of the coefficient
9 (3^2 = 9)
1

21. Scientific notation requires there to be only
Same base
10^-18
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.
one digit to the left of the decimal point

22. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
1. Multiply the coefficients 2. Add the exponents
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Same base

23. For the 10
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
exponent
Same base

24. Negative cube roots are okay ... negative square roots are
10^1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Not
proper scientific

25. 5^1 =
5
2
base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

26. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
1
When the exponent of a power-of-10 expression is a negative integer:
itself

27. Any number with an exponent of 0 is equal to
decrease the value of the exponent by 1 (dividing by 10)
1
same exponent
a fractional decimal

28. When you move the decimal point in the coefficient to the left
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
increase the power-of-10 exponent by the same number of units
Moving the decimal point to the right
1. Divide the coefficients 2. Subtract the exponents

29. 100 - or 1 with the decimal point moved two places to the right
10^2
negative number
1
increase the power-of-10 exponent by the same number of units

30. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
must be multiples of 3 or 0
rewrite one of the terms so that the exponents are equal
1 divided by that number with a positive exponent

31. 0 to any power is equal to
Step 1. Divide the coefficients of the terms
1. Multiply the coefficients 2. Add the exponents
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.
0

32. When you decrease the value of the power-of-10 exponent
perfect square
move the decimal point the same number of units to the right
decrease the value of the exponent by 1 (dividing by 10)
itself

33. 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
9 (3^2 = 9)
same exponent
When the exponent of a power-of-10 expression is a negative integer:
exponent

34.
10^1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
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

35. When you change the position of the decimal point in a coefficient value
Moving the decimal point to the right
Calculator square-root key
one digit to the left of the decimal point
you have to adjust the value of the exponent in order avoid changing the actual value.

36. There are no special rules for adding and subtracting numbers that are written with exponents.
rewrite one of the terms so that the exponents are equal
base
When the exponent of a power-of-10 expression is a negative integer:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

37. 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.
1
perfect square
base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

38. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
you have to adjust the value of the exponent in order avoid changing the actual value.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
square root

39. Increase the value of the exponent by 1 (multiplying by 10)
negative number
10^-18
When moving the decimal point to the left (dividing by 10)
one digit to the left of the decimal point

40. The decimal part
coefficient
square root
change both terms in order to keep the value the same.
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.

41. Any number with an exponent of 1 is equal to
1
itself
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Engineering notation

42. 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
coefficient
negative number
adjust the value of the coefficient
proper scientific

43. When moving the decimal point to the right (multiplying by 10)
1
decrease the value of the exponent by 1 (dividing by 10)
1
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

44. To divide powers that have the same base:
same exponent
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1
2

45. A negative exponent does not mean the decimal value is negative. It means the decimal value is
To multiply powers that have the same base:
Calculator square-root key
a fractional decimal
1

46. To add powers of ten:
change both terms in order to keep the value the same.
cube root
Because 4 multiplied by itself equals 16.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

47. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
10^-18
negative number
proper scientific

48. 10 - or 1 with the decimal point moved one place to the right
To multiply powers that have the same base:
10^1
10^-2
a fractional decimal

49. A number - when multiplied by itself - is equal to a given number.
Same base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
square root
1. Divide the coefficients 2. Subtract the exponents

50. Indicates the number to be multiplied.
10^2
base
1. Multiply the coefficients 2. Add the exponents
0