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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. 0^5 =
Engineering notation
9 (3^2 = 9)
0
Step 1. Divide the coefficients of the terms

2. Indicates the number to be multiplied.
move the decimal point the same number of units to the left
1
base
Moving the decimal point to the right

3. 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:
1 divided by that number with a positive exponent
base
10^-1

4. Negative cube roots are okay ... negative square roots are
1 divided by that number with a positive exponent
To multiply powers that have the same base:
Not
0

5. 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.
negative number
10^2
Engineering notation
Subtract the exponent

6. The square of 3 is
exponent
a fractional decimal
Engineering notation
9 (3^2 = 9)

7. To add or subtract numbers written with exponents:
Scientific notation
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
cube-root key
1. Divide the coefficients 2. Subtract the exponents

8. The square root of zero is
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
cube-root key

9. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
rewrite one of the terms so that the exponents are equal
1

10. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
1
adjust the value of the coefficient
5

11. Any number with a negative exponent is equal to
0
1 divided by that number with a positive exponent
10^-1
one digit to the left of the decimal point

12. Represents 1 preceded by 17 zeros and a decimal point.
Are Equal
10^-18
0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

13. To multiply or divide exponent terms that do not have the same base:
Because 4 multiplied by itself equals 16.
The solution exists - but not in the real number system.
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
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

14. When you move the decimal point in the coefficient to the left
Same base
increase the power-of-10 exponent by the same number of units
rewrite one of the terms so that the exponents are equal
Moving the decimal point to the left

15. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the right
3
10^1
move the decimal point the same number of units to the left

16. A number - when multiplied by itself - is equal to a given number.
a fractional decimal
adjust the value of the coefficient
cube root
square root

17. A number with an exponent of 3 is often said to be
change both terms in order to keep the value the same.
cubed
exponent
10^1

18. 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
proper scientific

19. The cube root of a negative number is also a
negative number
you have to adjust the value of the exponent in order avoid changing the actual value.
exponent
1

20. 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
Calculator square-root key
change both terms in order to keep the value the same.
increase the power-of-10 exponent by the same number of units
1. Multiply the coefficients 2. Add the exponents

21. To find the square root of any number - simply key in the number (the radicand) and press the
10^-1
The solution exists - but not in the real number system.
square root
Calculator square-root key

22. = 0.01 - or 1 with the decimal point moved two places to the left.
3
10^-2
1. Multiply the coefficients 2. Add the exponents
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

23. 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
the radical sign with a little 3 that indicates the cube root:
Because 4 multiplied by itself equals 16.
one digit to the left of the decimal point

24. Increase the value of the exponent by 1 (multiplying by 10)
1. Divide the coefficients 2. Subtract the exponents
When moving the decimal point to the left (dividing by 10)
0
10^-18

25. To divide powers of ten:
move the decimal point the same number of units to the left
10^1
1. Divide the coefficients 2. Subtract the exponents
itself

26. To divide powers that have the same base:
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1. Divide the coefficients 2. Subtract the exponents
1

27. Powers of ten can be added or subtracted only when their exponents
1
Are Equal
decrease the value of the exponent by 1 (dividing by 10)
Subtract the exponent

28. 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.
perfect square
1
increase the power-of-10 exponent by the same number of units
9 (3^2 = 9)

29. Any number with an exponent of 1 is equal to
itself
cube root
square root
move the decimal point the same number of units to the right

30. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1
change both terms in order to keep the value the same.

31. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
Scientific notation
a fractional decimal
To multiply powers that have the same base:

32. Multiplying by 10
squared
Moving the decimal point to the right
cubed
Are Equal

33. 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
3
decrease the power-of-10 exponent by the same number of units
Calculator square-root key

34. When you decrease the value of the power-of-10 exponent
change both terms in order to keep the value the same.
move the decimal point the same number of units to the right
cubed
Same base

35. Indicates the number of times the base is to be multiplied.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
0
exponent
cube-root key

36. What number multiplied by itself is equal to 16? The answer is 4. Why?
3
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
must be multiples of 3 or 0
Because 4 multiplied by itself equals 16.

37. 0 to any power is equal to
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
proper scientific
0

38. 100 - or 1 with the decimal point moved two places to the right
base
10^2
0
1

39. 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.
Moving the decimal point to the right
radical sign
Subtract the exponent
3

40. A number with an exponent of 2 is often said to be
1
Subtract the exponent
squared
decrease the value of the exponent by 1 (dividing by 10)

41. To multiply powers of 10:
10^2
decrease the value of the exponent by 1 (dividing by 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.
2 x 10^9

42. 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
Engineering notation
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
square root

43. To subtract powers of ten:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Engineering notation
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

44. 10 - or 1 with the decimal point moved one place to the right
cubed
10^1
negative number
1 divided by that number with a positive exponent

45. Any number with an exponent of 0 is equal to
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
decrease the power-of-10 exponent by the same number of units
cube-root key

46. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
the radical sign with a little 3 that indicates the cube root:
To multiply powers that have the same base:
proper scientific
9 (3^2 = 9)

47. Numbers with exponents can be directly multiplied or divided only when they have the
Same base
1
The solution exists - but not in the real number system.
base

48. 1^4 =
move the decimal point the same number of units to the left
Moving the decimal point to the right
1
Because 4 multiplied by itself equals 16.

49. 5^1 =
a fractional decimal
negative number
5
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

50. 1 to any power is equal to
1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
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
3