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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. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1
increase the power-of-10 exponent by the same number of units
exponent

2. To find the square root of any number - simply key in the number (the radicand) and press the
change both terms in order to keep the value the same.
1
Calculator square-root key
a fractional decimal

3. When you change the position of the decimal point in a coefficient value
square root
When the exponent of a power-of-10 expression is a negative integer:
The solution exists - but not in the real number system.
you have to adjust the value of the exponent in order avoid changing the actual value.

4. A number with an exponent of 3 is often said to be
cubed
Calculator square-root key
10^-18
9 (3^2 = 9)

5. Numbers with exponents can be directly multiplied or divided only when they have the
one digit to the left of the decimal point
cube-root key
10^-2
Same base

6. Indicates the number of times the base is to be multiplied.
To multiply powers that have the same base:
square root
Not
exponent

7. To multiply powers of 10:
9 (3^2 = 9)
Moving the decimal point to the right
square root
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.

8. To divide powers of ten:
The solution exists - but not in the real number system.
1. Divide the coefficients 2. Subtract the exponents
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
To multiply powers that have the same base:

9. When you increase the value of the power-of-10 exponent
1
move the decimal point the same number of units to the left
10^-18
The solution exists - but not in the real number system.

10. 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
1
radical sign
10^-1

11. The decimal part
perfect square
coefficient
1 divided by that number with a positive exponent
itself

12. A very small number such as 0.000000674 can be written with scientific notation as
2 x 10^9
6.74 x 10^-7
When the exponent of a power-of-10 expression is a negative integer:
adjust the value of the coefficient

13. When you move the decimal point in the coefficient to the right
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
1. Multiply the coefficients 2. Add the exponents
decrease the power-of-10 exponent by the same number of units

14. 1 to any power is equal to
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
adjust the value of the coefficient
3

15. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
When moving the decimal point to the left (dividing by 10)
Moving the decimal point to the left
coefficient

16. 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
10^2
cube-root key
move the decimal point the same number of units to the left
must be multiples of 3 or 0

17. To multiply powers of ten:
Are Equal
Moving the decimal point to the left
Moving the decimal point to the right
1. Multiply the coefficients 2. Add the exponents

18. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
10^2
1. Divide the coefficients 2. Subtract the exponents
0

19. A number with an exponent of 2 is often said to be
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
squared
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.
square root

20. Valid powers of 10 for engineering notation are:
10^-18
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Because 4 multiplied by itself equals 16.
Calculator square-root key

21. Always 10 for scientific notation
Scientific notation
1. Divide the coefficients 2. Subtract the exponents
same exponent
base

22. To subtract powers of ten:
radical sign
Moving the decimal point to the right
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0

23. Valid powers-of-10 for engineering notation
When the exponent of a power-of-10 expression is a negative integer:
0
must be multiples of 3 or 0
base

24. To divide powers of 10:
1 divided by that number with a positive exponent
Step 1. Divide the coefficients of the terms
0
9 (3^2 = 9)

25. Powers of ten can be added or subtracted only when their exponents
1
one digit to the left of the decimal point
cube root
Are Equal

26. To add or subtract numbers written with exponents:
one digit to the left of the decimal point
cube root
1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

27. Any number with an exponent of 0 is equal to
10^1
decrease the value of the exponent by 1 (dividing by 10)
1
10^-2

28. 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.
10^-2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Engineering notation
decrease the value of the exponent by 1 (dividing by 10)

29. Multiplying by 10
10^-1
Moving the decimal point to the right
exponent
5

30. = 0.1 - or 1 with the decimal point moved one place to the left.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-1
increase 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

31. Indicates the number to be multiplied.
5
base
squared
When the exponent of a power-of-10 expression is a negative integer:

32. 1 to any power is equal to
0
10^-18
1
Moving the decimal point to the right

33. 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:
exponent
increase the power-of-10 exponent by the same number of units
the radical sign with a little 3 that indicates the cube root:

34. 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
squared
decrease the power-of-10 exponent by the same number of units
10^2

35. Any number with an exponent of 1 is equal to
9 (3^2 = 9)
1
1. Divide the coefficients 2. Subtract the exponents
itself

36. The cube root of a negative number is also a
increase the power-of-10 exponent by the same number of units
negative number
2
Engineering notation

37. 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
negative number
coefficient
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
adjust the value of the coefficient

38. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
coefficient
a fractional decimal
base
2 x 10^9

39. 3^0 =
Moving the decimal point to the left
1
0
10^-1

40. What number multiplied by itself is equal to 16? The answer is 4. Why?
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Because 4 multiplied by itself equals 16.
10^-2
Step 1. Divide the coefficients of the terms

41. 0^5 =
square root
0
adjust the value of the coefficient
cube-root key

42. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
1
9 (3^2 = 9)
radical sign

43. = 0.01 - or 1 with the decimal point moved two places to the left.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-2
exponent
Calculator square-root key

44. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1. Divide the coefficients 2. Subtract the exponents
cubed
0
2

45. Dividing by 10
Moving the decimal point to the left
0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
0

46. 5^1 =
5
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
squared
decrease the power-of-10 exponent by the same number of units

47. 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
decrease the value of the exponent by 1 (dividing by 10)
1
0
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

48. A number is a second number which - when multiplied by itself three times - equals the original number.
coefficient
cube root
6.74 x 10^-7
base

49. Represents 1 preceded by 17 zeros and a decimal point.
10^-1
Because 4 multiplied by itself equals 16.
10^-18
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

50. 100 - or 1 with the decimal point moved two places to the right
0
10^2
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Not