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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 multiply or divide exponent terms that do not have the same base:
decrease the value of the exponent by 1 (dividing by 10)
rewrite one of the terms so that the exponents are equal
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Same base

2. Don't bother trying to find the square root of a negative number.
Scientific notation
The solution exists - but not in the real number system.
one digit to the left of the decimal point
Calculator square-root key

3. = 0.1 - or 1 with the decimal point moved one place to the left.
5
9 (3^2 = 9)
0
10^-1

4. To divide powers of 10:
1. Multiply the coefficients 2. Add the exponents
Step 1. Divide the coefficients of the terms
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.

5.
perfect square
itself
a fractional decimal
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

6. 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
negative number
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
adjust the value of the coefficient

7. 1 to any power is equal to
10^2
coefficient
exponent
1

8. To subtract powers of ten:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
decrease the power-of-10 exponent by the same number of units
1

9. A number with an exponent of 2 is often said to be
1
negative number
squared
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

10. Indicates the number of times the base is to be multiplied.
exponent
0
cubed
proper scientific

11. 1 to any power is equal to
cubed
1
Moving the decimal point to the right
Moving the decimal point to the left

12. The cube root of a negative number is also a
negative number
Subtract the exponent
1. Multiply the coefficients 2. Add the exponents
1

13. 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.
When the exponent of a power-of-10 expression is a negative integer:
one digit to the left of the decimal point
change both terms in order to keep the value the same.
cubed

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

15. Step 1: Add the exponents Step 2: Use the common base
squared
To multiply powers that have the same base:
6.74 x 10^-7
Subtract the exponent

16. Negative cube roots are okay ... negative square roots are
Not
6.74 x 10^-7
cube root
one digit to the left of the decimal point

17. 3^0 =
When moving the decimal point to the left (dividing by 10)
The solution exists - but not in the real number system.
1
2 x 10^9

18. Multiplying by 10
The solution exists - but not in the real number system.
9 (3^2 = 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
Moving the decimal point to the right

19. 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.
increase the power-of-10 exponent by the same number of units
cube-root key
exponent
perfect square

20. Powers of ten can be added or subtracted only when their exponents
move the decimal point the same number of units to the left
perfect square
Are Equal
cube root

21. 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
change both terms in order to keep the value the same.
5
10^-2
same exponent

22. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
Moving the decimal point to the left
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
To multiply powers that have the same base:

23. Dividing by 10
When the exponent of a power-of-10 expression is a negative integer:
cubed
square root
Moving the decimal point to the left

24. Represents 1 preceded by 17 zeros and a decimal point.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
coefficient
Moving the decimal point to the left
10^-18

25. To add or subtract numbers written with 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.
Because 4 multiplied by itself equals 16.
To multiply powers that have the same base:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

26. There are no special rules for adding and subtracting numbers that are written with exponents.
10^2
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
increase the power-of-10 exponent by the same number of units
9 (3^2 = 9)

27. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
Moving the decimal point to the right
5
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

28. When you increase the value of the power-of-10 exponent
exponent
move the decimal point the same number of units to the left
1. Multiply the coefficients 2. Add the exponents
change both terms in order to keep the value the same.

29. A number with an exponent of 3 is often said to be
cubed
1
Not
10^-18

30. 0 to any power is equal to
Not
adjust the value of the coefficient
0
base

31. To divide powers of ten:
3
decrease the value of the exponent by 1 (dividing by 10)
1
1. Divide the coefficients 2. Subtract the exponents

32. When you change the position of the decimal point in a coefficient value
Moving the decimal point 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.
radical sign
you have to adjust the value of the exponent in order avoid changing the actual value.

33. A number - when multiplied by itself - is equal to a given number.
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
To multiply powers that have the same base:
square root
move the decimal point the same number of units to the right

34. The square root of zero is
0
10^-1
Engineering notation
cube-root key

35. The decimal part
move the decimal point the same number of units to the right
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
coefficient
1. Multiply the coefficients 2. Add the exponents

36. 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.
2 x 10^9
radical sign
the radical sign with a little 3 that indicates the cube root:
you have to adjust the value of the exponent in order avoid changing the actual value.

37. When the exponents are not the same
increase the power-of-10 exponent by the same number of units
cubed
rewrite one of the terms so that the exponents are equal
you have to adjust the value of the exponent in order avoid changing the actual value.

38. 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
you have to adjust the value of the exponent in order avoid changing the actual value.
1
same exponent
To multiply powers that have the same base:

39. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
cubed
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
10^-18
2

40. 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
3
same exponent
cube-root key
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

41. A negative exponent does not mean the decimal value is negative. It means the decimal value is
1. Multiply the coefficients 2. Add the exponents
adjust the value of the coefficient
a fractional decimal
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

42. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
10^-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
Are Equal
proper scientific

43. 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. Divide the coefficients 2. Subtract the exponents
decrease the power-of-10 exponent by the same number of units
cube-root key
Engineering notation

44. 100 - or 1 with the decimal point moved two places to the right
coefficient
1. Multiply the coefficients 2. Add the exponents
10^2
increase the power-of-10 exponent by the same number of units

45. 10 - or 1 with the decimal point moved one place to the right
same exponent
5
To multiply powers that have the same base:
10^1

46. 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
5
itself
cube-root key
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

47. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
1
Subtract the exponent
Same base

48. Scientific notation requires there to be only
Same base
one digit to the left of the decimal point
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
base

49. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
1
base
move the decimal point the same number of units to the right

50. Valid powers of 10 for engineering notation are:
1
10^-18
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
radical sign