Test your basic knowledge |

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. Scientific notation requires there to be only
one digit to the left of the decimal point
increase the power-of-10 exponent by the same number of units
decrease the power-of-10 exponent by the same number of units
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

2. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
Moving the decimal point to the left
To multiply powers that have the same base:
negative number

3. The square root of zero is
1
Moving the decimal point to the right
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
0

4. 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
decrease the power-of-10 exponent by the same number of units
itself
change both terms in order to keep the value the same.
coefficient

5. To subtract powers of ten:
Because 4 multiplied by itself equals 16.
2
Subtract the exponent
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

6. For the 10
2
exponent
The solution exists - but not in the real number system.
0

7. 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.
When the exponent of a power-of-10 expression is a negative integer:
1 divided by that number with a positive exponent
Not
radical sign

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

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
negative number
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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
adjust the value of the coefficient

10. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^-2
10^1

11. The cube root of zero is
0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Subtract the exponent
To multiply powers that have the same base:

12. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
2 x 10^9
When moving the decimal point to the left (dividing by 10)
10^1
Subtract the exponent

13. 1^4 =
Moving the decimal point to the left
1
1. Divide the coefficients 2. Subtract the exponents
9 (3^2 = 9)

14. Don't bother trying to find the square root of a negative 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
Engineering notation
1
The solution exists - but not in the real number system.

15. To multiply or divide exponent terms that do not have the same base:
cube root
Scientific notation
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1

16. 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.
Are Equal
When the exponent of a power-of-10 expression is a negative integer:
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
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

17. When you move the decimal point in the coefficient to the left
2
Because 4 multiplied by itself equals 16.
5
increase the power-of-10 exponent by the same number of units

18. To add or subtract numbers written with exponents:
the radical sign with a little 3 that indicates the cube root:
10^-2
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
radical sign

19. Any number with an exponent of 0 is equal to
1
negative number
a fractional decimal
rewrite one of the terms so that the exponents are equal

20. 5^1 =
squared
exponent
When the exponent of a power-of-10 expression is a negative integer:
5

21. A number is a second number which - when multiplied by itself three times - equals the original number.
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
proper scientific
cube root

22. 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
adjust the value of the coefficient
same exponent
9 (3^2 = 9)
perfect square

23. Dividing by 10
coefficient
Moving the decimal point to the left
10^-2
10^-18

24. A very small number such as 0.000000674 can be written with scientific notation as
To multiply powers that have the same base:
6.74 x 10^-7
coefficient
Subtract the exponent

25. The square root of 9 is
3
Engineering notation
Subtract the exponent
radical sign

26. 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.
Engineering notation
The solution exists - but not in the real number system.
negative number
Scientific notation

27. 3^0 =
Subtract the exponent
Moving the decimal point to the left
Calculator square-root key
1

28. To multiply powers of 10:
radical sign
Calculator square-root key
base
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.

29. Powers of ten can be added or subtracted only when their exponents
Are Equal
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
base
decrease the value of the exponent by 1 (dividing by 10)

30. = 0.1 - or 1 with the decimal point moved one place to the left.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
coefficient
10^-1
The solution exists - but not in the real number system.

31. Step 1: Add the exponents Step 2: Use the common base
Step 1. Divide the coefficients of the terms
When the exponent of a power-of-10 expression is a negative integer:
To multiply powers that have the same base:
2 x 10^9

32. 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
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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
1. Multiply the coefficients 2. Add the exponents

33. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
6.74 x 10^-7
1. Multiply the coefficients 2. Add the exponents
10^-2

34. To divide powers that have the same base:
Step 1. Divide the coefficients of the terms
Calculator square-root key
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
must be multiples of 3 or 0

35. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
Step 1. Divide the coefficients of the terms
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
must be multiples of 3 or 0

36. 100 - or 1 with the decimal point moved two places to the right
cubed
10^2
0
a fractional decimal

37. A number - when multiplied by itself - is equal to a given number.
square root
proper scientific
10^2
Same base

38. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
base
5
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

39. 1 to any power is equal to
adjust the value of the coefficient
1
Step 1. Divide the coefficients of the terms
3

40. When moving the decimal point to the right (multiplying by 10)
adjust the value of the coefficient
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
decrease the value of the exponent by 1 (dividing by 10)
Scientific notation

41. There are no special rules for adding and subtracting numbers that are written with exponents.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
10^1
decrease the value of the exponent by 1 (dividing by 10)
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

42. Always 10 for scientific notation
When moving the decimal point to the left (dividing by 10)
base
0
10^1

43. To divide powers of 10:
Step 1. Divide the coefficients of the terms
10^-2
3
exponent

44. 0^5 =
cube-root key
1
0
Same base

45. Numbers with exponents can be directly multiplied or divided only when they have the
Engineering notation
Because 4 multiplied by itself equals 16.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Same base

46. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
1. Divide the coefficients 2. Subtract the exponents
10^-2
Moving the decimal point to the right

47. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
1
Step 1. Divide the coefficients of the terms
0

48. 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.
Step 1. Divide the coefficients of the terms
perfect square
exponent
9 (3^2 = 9)

49. A number with an exponent of 2 is often said to be
squared
square root
Not
0

50. To find the square root of any number - simply key in the number (the radicand) and press the
Calculator square-root key
0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1. Divide the coefficients 2. Subtract the exponents