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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. A number with an exponent of 2 is often said to be
Scientific notation
10^-18
When the exponent of a power-of-10 expression is a negative integer:
squared

2. To multiply powers of ten:
10^2
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1. Multiply the coefficients 2. Add the exponents
must be multiples of 3 or 0

3. Don't bother trying to find the square root of a negative number.
Engineering notation
The solution exists - but not in the real number system.
1. Multiply the coefficients 2. Add the exponents
negative number

4. 1 to any power is equal to
negative number
Calculator square-root key
Are Equal
1

5. Step 1: Add the exponents Step 2: Use the common base
9 (3^2 = 9)
1
To multiply powers that have the same base:
10^-18

6. 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
When the exponent of a power-of-10 expression is a negative integer:
2 x 10^9
1

7. 0 to any power is equal to
0
Step 1. Divide the coefficients of the terms
base
exponent

8. Always 10 for scientific notation
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.
base
Moving the decimal point to the left

9. Dividing by 10
negative number
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Moving the decimal point to the left
5

10. When the exponents are not the same
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
rewrite one of the terms so that the exponents are equal
10^-18
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

11. 3^0 =
10^-2
1
1. Divide the coefficients 2. Subtract the exponents
negative number

12. 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.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
same exponent
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

13. 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.
decrease the power-of-10 exponent by the same number of units
Moving the decimal point to the right
exponent
Scientific notation

14. 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
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
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

15. 100 - or 1 with the decimal point moved two places to the right
When moving the decimal point to the left (dividing by 10)
5
10^2
1. Multiply the coefficients 2. Add the exponents

16. A number with an exponent of 3 is often said to be
cubed
0
proper scientific
1

17. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
coefficient
The solution exists - but not in the real number system.
Scientific notation

18. The cube root of a negative number is also a
negative number
Engineering notation
0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

19. 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.
must be multiples of 3 or 0
10^2
10^-2
radical sign

20. The decimal part
2 x 10^9
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Because 4 multiplied by itself equals 16.
coefficient

21. To find the square root of any number - simply key in the number (the radicand) and press the
1. Multiply the coefficients 2. Add the exponents
5
Because 4 multiplied by itself equals 16.
Calculator square-root key

22. There are no special rules for adding and subtracting numbers that are written with exponents.
move the decimal point the same number of units to the left
square root
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
you have to adjust the value of the exponent in order avoid changing the actual value.

23. Indicates the number to be multiplied.
1. Divide the coefficients 2. Subtract the exponents
base
10^1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

24. 5^1 =
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
0
Engineering notation
5

25. A number is a second number which - when multiplied by itself three times - equals the original number.
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
cube root
one digit to the left of the decimal point

26. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
0
adjust the value of the coefficient
10^-1

27. 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
same exponent
1. Divide the coefficients 2. Subtract the exponents
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

28. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
10^-18
10^-1
same exponent

29. To add or subtract numbers written with exponents:
perfect square
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

30. When you move the decimal point in the coefficient to the right
Subtract the exponent
adjust the value of the coefficient
square root
decrease the power-of-10 exponent by the same number of units

31. 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.
Calculator square-root key
0
When the exponent of a power-of-10 expression is a negative integer:
10^1

32. Represents 1 preceded by 17 zeros and a decimal point.
1. Divide the coefficients 2. Subtract the exponents
Calculator square-root key
2
10^-18

33. A very small number such as 0.000000674 can be written with scientific notation as
1
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
6.74 x 10^-7

34. 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
change both terms in order to keep the value the same.
decrease the value of the exponent by 1 (dividing by 10)
3

35. 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.
5
cubed
Engineering notation
decrease the value of the exponent by 1 (dividing by 10)

36. = 0.1 - or 1 with the decimal point moved one place to the left.
Because 4 multiplied by itself equals 16.
10^-1
1
6.74 x 10^-7

37. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
Scientific notation
1. Divide the coefficients 2. Subtract the exponents
cube root

38. 1 to any power is equal to
6.74 x 10^-7
1
coefficient
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

39. The cube root of zero is
Are Equal
Calculator square-root key
0
Subtract the exponent

40. Multiplying by 10
Moving the decimal point to the right
10^-2
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Because 4 multiplied by itself equals 16.

41. The square root of 9 is
3
When the exponent of a power-of-10 expression is a negative integer:
1. Multiply the coefficients 2. Add the exponents
must be multiples of 3 or 0

42. The square root of zero is
1. Multiply the coefficients 2. Add the exponents
0
squared
Calculator square-root key

43. Numbers with exponents can be directly multiplied or divided only when they have the
1
Same base
Step 1. Divide the coefficients of the terms
10^-18

44. 0^5 =
10^-1
coefficient
adjust the value of the coefficient
0

45. To multiply powers of 10:
same 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.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
squared

46. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
10^-2
cube root
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
2 x 10^9

47. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
2 x 10^9
exponent
exponent

48. 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
negative number
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
square root

49. The square of 3 is
9 (3^2 = 9)
Moving the decimal point to the left
Engineering notation
cubed

50. Valid powers of 10 for engineering notation are:
decrease the power-of-10 exponent by the same number of units
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Scientific notation
When the exponent of a power-of-10 expression is a negative integer: