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. The square root of zero is
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.
When moving the decimal point to the left (dividing by 10)
a fractional decimal
0

2. What number multiplied by itself is equal to 16? The answer is 4. Why?
move the decimal point the same number of units to the left
Because 4 multiplied by itself equals 16.
must be multiples of 3 or 0
cube-root key

3. Any number with an exponent of 1 is equal to
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^2
itself
1

4. To multiply powers of ten:
0
one digit to the left of the decimal point
2
1. Multiply the coefficients 2. Add the exponents

5. The cube root of zero is
Subtract the exponent
0
must be multiples of 3 or 0
Because 4 multiplied by itself equals 16.

6. There are no special rules for adding and subtracting numbers that are written with exponents.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
negative number
rewrite one of the terms so that the exponents are equal
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

7. A number is a second number which - when multiplied by itself three times - equals the original number.
To multiply powers that have the same base:
cube root
Moving the decimal point to the right
base

8. 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.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
When the exponent of a power-of-10 expression is a negative integer:
1
1

9. Represents 1 preceded by 17 zeros and a decimal point.
you have to adjust the value of the exponent in order avoid changing the actual value.
10^-18
10^-1
0

10. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
one digit to the left of the decimal point
9 (3^2 = 9)
Are Equal

11. Any number with a negative exponent is equal to
change both terms in order to keep the value the same.
1. Divide the coefficients 2. Subtract the exponents
1 divided by that number with a positive exponent
1

12. A number with an exponent of 2 is often said to be
squared
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1 divided by that number with a positive exponent
5

13. 1 to any power is equal to
1
2
must be multiples of 3 or 0
Step 1. Divide the coefficients of the terms

14. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
cube-root key
1
Subtract the exponent

15. Negative cube roots are okay ... negative square roots are
cube root
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
Not
Are Equal

16. 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.
you have to adjust the value of the exponent in order avoid changing the actual value.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Scientific notation

17. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
base
base
The solution exists - but not in the real number system.

18. To add or subtract numbers written with exponents:
base
1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Scientific notation

19. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
the radical sign with a little 3 that indicates the cube root:
2
Moving the decimal point to the right

20. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
cube root
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
negative number

21. Dividing by 10
Are Equal
Not
Scientific notation
Moving the decimal point to the left

22. Any number with an exponent of 0 is equal to
adjust the value of the coefficient
6.74 x 10^-7
1
rewrite one of the terms so that the exponents are equal

23. The decimal part
coefficient
6.74 x 10^-7
move the decimal point the same number of units to the left
10^-2

24. The cube root of a negative number is also a
10^2
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
the radical sign with a little 3 that indicates the cube root:
negative number

25. Don't bother trying to find the square root of a negative number.
Engineering notation
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
The solution exists - but not in the real number system.
itself

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
10^2
perfect square
same exponent

27. 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
move the decimal point the same number of units to the right
increase the power-of-10 exponent by the same number of units
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

28. A number with an exponent of 3 is often said to be
base
5
itself
cubed

29. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Moving the decimal point to the right
To multiply powers that have the same base:
Subtract the exponent
When moving the decimal point to the left (dividing by 10)

30. To divide powers of 10:
1
same exponent
Step 1. Divide the coefficients of the terms
base

31. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Same base
proper scientific
Calculator square-root key
0

32. When the exponents are not the same
adjust the value of the coefficient
one digit to the left of the decimal point
proper scientific
rewrite one of the terms so that the exponents are equal

33. To multiply or divide exponent terms that do not have the same base:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
the radical sign with a little 3 that indicates the cube root:
1 divided by that number with a positive exponent
0

34. 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
Not
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
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
radical sign

35. Step 1: Add the exponents Step 2: Use the common base
radical sign
base
change both terms in order to keep the value the same.
To multiply powers that have the same base:

36. When you move the decimal point in the coefficient to the right
move the decimal point the same number of units to the left
change both terms in order to keep the value the same.
1. Multiply the coefficients 2. Add the exponents
decrease the power-of-10 exponent by the same number of units

37. To add powers of ten:
Because 4 multiplied by itself equals 16.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
rewrite one of the terms so that the exponents are equal

38. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-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
Not
decrease the value of the exponent by 1 (dividing by 10)

39. Numbers with exponents can be directly multiplied or divided only when they have the
negative number
rewrite one of the terms so that the exponents are equal
decrease the value of the exponent by 1 (dividing by 10)
Same base

40. 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
proper scientific
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
When the exponent of a power-of-10 expression is a negative integer:
adjust the value of the coefficient

41. When moving the decimal point to the right (multiplying by 10)
Moving the decimal point to the left
10^-1
move the decimal point the same number of units to the right
decrease the value of the exponent by 1 (dividing by 10)

42. 5^1 =
1
1
6.74 x 10^-7
5

43. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
0
Moving the decimal point to the left
2 x 10^9
square root

44. 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
move the decimal point the same number of units to the left
1
same exponent

45. When you increase the value of the power-of-10 exponent
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
move the decimal point the same number of units to the left
Same base

46. 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.
radical sign
5
change both terms in order to keep the value the same.
2

47. To find the square root of any number - simply key in the number (the radicand) and press the
Calculator square-root key
Moving the decimal point to the right
2
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

48. The square root of 9 is
you have to adjust the value of the exponent in order avoid changing the actual value.
10^2
3
9 (3^2 = 9)

49. 1 to any power is equal to
1
move the decimal point the same number of units to the right
1 divided by that number with a positive exponent
1. Multiply the coefficients 2. Add the exponents

50. 100 - or 1 with the decimal point moved two places to the right
change both terms in order to keep the value the same.
To multiply powers that have the same base:
10^2
itself