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CLEP General Mathematics: Powers Exponents And Roots

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. The square root of 9 is
cubed
rewrite one of the terms so that the exponents are equal
3
Calculator square-root key

2. 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.
3
1
the radical sign with a little 3 that indicates the cube root:

3. For the 10
proper scientific
10^2
increase the power-of-10 exponent by the same number of units
exponent

4. 1^4 =
one digit to the left of the decimal point
decrease the power-of-10 exponent by the same number of units
1
When the exponent of a power-of-10 expression is a negative integer:

5. A very small number such as 0.000000674 can be written with scientific notation as
Same base
Are Equal
1
6.74 x 10^-7

6. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
exponent
10^-2
Subtract the exponent
one digit to the left of the decimal point

7. The square of 3 is
decrease the power-of-10 exponent by the same number of units
9 (3^2 = 9)
0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

8. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
increase the power-of-10 exponent by the same number of units
rewrite one of the terms so that the exponents are equal
1. Multiply the coefficients 2. Add the exponents

9. 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.
0
9 (3^2 = 9)
base
radical sign

10. Dividing by 10
Moving the decimal point to the left
cubed
radical sign
2 x 10^9

11. To multiply powers of ten:
move the decimal point the same number of units to the left
Moving the decimal point to the right
proper scientific
1. Multiply the coefficients 2. Add the exponents

12. 3^0 =
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1
perfect square
3

13.
3
0
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

14. When you increase the value of the power-of-10 exponent
Not
move the decimal point the same number of units to the left
base
move the decimal point the same number of units to the right

15. Indicates the number to be multiplied.
a fractional decimal
Are Equal
base
cube-root key

16. When you decrease the value of the power-of-10 exponent
1
move the decimal point the same number of units to the right
1
must be multiples of 3 or 0

17. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
The solution exists - but not in the real number system.
adjust the value of the coefficient
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

18. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
2 x 10^9
5
The solution exists - but not in the real number system.

19. 5^1 =
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
cube root
5
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.

20. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
10^-2
0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

21. To divide powers of 10:
Engineering notation
adjust the value of the coefficient
Step 1. Divide the coefficients of the terms
0

22. Represents 1 preceded by 17 zeros and a decimal point.
0
10^-18
When moving the decimal point to the left (dividing by 10)
Scientific notation

23. When the exponents are not the same
Moving the decimal point to the right
a fractional decimal
rewrite one of the terms so that the exponents are equal
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

24. 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
Subtract the exponent
square root
same exponent
1. Divide the coefficients 2. Subtract the exponents

25. A number with an exponent of 2 is often said to be
squared
0
0
Scientific notation

26. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
Subtract the exponent
Moving the decimal point to the right
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

27. To add powers of ten:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0
one digit to the left of the decimal point
Are Equal

28. 100 - or 1 with the decimal point moved two places to the right
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
10^2
the radical sign with a little 3 that indicates the cube root:

29. = 0.01 - or 1 with the decimal point moved two places to the left.
9 (3^2 = 9)
must be multiples of 3 or 0
10^-2
When the exponent of a power-of-10 expression is a negative integer:

30. To find the square root of any number - simply key in the number (the radicand) and press the
Calculator square-root key
exponent
Subtract the exponent
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

31. Step 1: Add the exponents Step 2: Use the common base
10^2
exponent
To multiply powers that have the same base:
negative number

32. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Are Equal
squared
coefficient
a fractional decimal

33. 0 to any power is equal to
0
1
Moving the decimal point to the right
Step 1. Divide the coefficients of the terms

34. To add or subtract numbers written with exponents:
6.74 x 10^-7
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Divide the coefficients of the terms
proper scientific

35. 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.
6.74 x 10^-7
base
perfect square

36. Multiplying by 10
one digit to the left of the decimal point
Moving the decimal point to the right
1
increase the power-of-10 exponent by the same number of units

37. 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.
1 divided by that number with a positive exponent
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.
perfect square
Scientific notation

38. 1 to any power is equal to
decrease the power-of-10 exponent by the same number of units
move the decimal point the same number of units to the right
1
0

39. 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
square root
When moving the decimal point to the left (dividing by 10)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
adjust the value of the coefficient

40. 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.
itself
1
must be multiples of 3 or 0
Engineering notation

41. There are no special rules for adding and subtracting numbers that are written with exponents.
coefficient
0
To multiply powers that have the same base:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

42. Always 10 for scientific notation
Scientific notation
base
cubed
When the exponent of a power-of-10 expression is a negative integer:

43. The decimal part
1
2 x 10^9
proper scientific
coefficient

44. 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.
3
0
When the exponent of a power-of-10 expression is a negative integer:
base

45. A number with an exponent of 3 is often said to be
2 x 10^9
cubed
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
10^1

46. When you change the position of the decimal point in a coefficient value
6.74 x 10^-7
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.
perfect square
you have to adjust the value of the exponent in order avoid changing the actual value.

47. Don't bother trying to find the square root of a negative number.
The solution exists - but not in the real number system.
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.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^2

48. Powers of ten can be added or subtracted only when their exponents
Moving the decimal point to the right
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

49. To subtract powers of ten:
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
perfect square
a fractional decimal

50. Negative cube roots are okay ... negative square roots are
cube-root key
Engineering notation
Not
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.