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. 1 to any power is equal to
Subtract the exponent
1
When the exponent of a power-of-10 expression is a negative integer:
2 x 10^9

2. A number with an exponent of 3 is often said to be
0
cubed
base
1. Divide the coefficients 2. Subtract the exponents

3. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
1. Multiply the coefficients 2. Add the exponents
2 x 10^9
perfect square
decrease the power-of-10 exponent by the same number of units

4. Any number with an exponent of 1 is equal to
0
itself
Moving the decimal point 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

5. 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
proper scientific
Are Equal
cube-root key
move the decimal point the same number of units to the left

6. Represents 1 preceded by 17 zeros and a decimal point.
change both terms in order to keep the value the same.
10^-18
1
5

7. To multiply or divide exponent terms that do not have the same base:
coefficient
10^1
adjust the value of the coefficient
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

8. Powers of ten can be added or subtracted only when their exponents
Engineering notation
1
Are Equal
squared

9. 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. Multiply the coefficients 2. Add the exponents
Moving the decimal point to the right
must be multiples of 3 or 0

10. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
squared
2
radical sign
square root

11. To divide powers of 10:
decrease the value of the exponent by 1 (dividing by 10)
Step 1. Divide the coefficients of the terms
rewrite one of the terms so that the exponents are equal
10^-18

12. To divide powers that have the same base:
When the exponent of a power-of-10 expression is a negative integer:
Calculator square-root key
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

13. 100 - or 1 with the decimal point moved two places to the right
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
10^2
10^-2
1

14. 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.
10^-18
When the exponent of a power-of-10 expression is a negative integer:
move the decimal point the same number of units to the right
negative number

15. Dividing by 10
Moving the decimal point to the left
0
6.74 x 10^-7
Engineering notation

16. 10 - or 1 with the decimal point moved one place to the right
1. Multiply the coefficients 2. Add the exponents
decrease the value of the exponent by 1 (dividing by 10)
10^1
6.74 x 10^-7

17. When the exponents are not the same
Moving the decimal point to the right
When moving the decimal point to the left (dividing by 10)
1. Divide the coefficients 2. Subtract the exponents
rewrite one of the terms so that the exponents are equal

18. To add powers of ten:
1
1 divided by that number with a positive exponent
rewrite one of the terms so that the exponents are equal
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

19. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1 divided by that number with a positive exponent
10^-18

20. 1 to any power is equal to
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
To multiply powers that have the same base:
Scientific notation
1

21. The square root of 9 is
radical sign
1. Divide the coefficients 2. Subtract the exponents
3
Moving the decimal point to the right

22. 0 to any power is equal to
cube-root key
Moving the decimal point to the left
itself
0

23. Any number with an exponent of 0 is equal to
1. Multiply the coefficients 2. Add the exponents
Scientific notation
1
negative number

24.
1
10^-18
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

25. = 0.1 - or 1 with the decimal point moved one place to the left.
0
10^2
10^-1
When moving the decimal point to the left (dividing by 10)

26. Step 1: Add the exponents Step 2: Use the common base
decrease the value of the exponent by 1 (dividing by 10)
must be multiples of 3 or 0
To multiply powers that have the same base:
9 (3^2 = 9)

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.
1 divided by that number with a positive exponent
perfect square
cubed
you have to adjust the value of the exponent in order avoid changing the actual value.

28. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
Scientific notation
exponent
10^-18

29. The cube root of a negative number is also a
negative number
1
you have to adjust the value of the exponent in order avoid changing the actual value.
10^-1

30. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
When moving the decimal point to the left (dividing by 10)
2 x 10^9
a fractional decimal

31. 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
10^2
must be multiples of 3 or 0
1

32. When you move the decimal point in the coefficient to the right
cube root
move the decimal point the same number of units to the right
same exponent
decrease the power-of-10 exponent by the same number of units

33. 0^5 =
Moving the decimal point to the right
squared
When the exponent of a power-of-10 expression is a negative integer:
0

34. The cube root of zero is
adjust the value of the coefficient
0
cubed
Are Equal

35. There are no special rules for adding and subtracting numbers that are written with exponents.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
square root
Not
The solution exists - but not in the real number system.

36. 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
base
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
Subtract the exponent
exponent

37. To divide powers of ten:
To multiply powers that have the same base:
1. Divide the coefficients 2. Subtract the exponents
move the decimal point the same number of units to the right
increase the power-of-10 exponent by the same number of units

38. A number - when multiplied by itself - is equal to a given number.
exponent
decrease the power-of-10 exponent by the same number of units
To multiply powers that have the same base:
square root

39. Indicates the number of times the base is to be multiplied.
exponent
When moving the decimal point to the left (dividing by 10)
6.74 x 10^-7
0

40. Numbers with exponents can be directly multiplied or divided only when they have the
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
Same base
10^-2
0

41. The square of 3 is
2 x 10^9
adjust the value of the coefficient
9 (3^2 = 9)
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

42. 3^0 =
square root
1
move the decimal point the same number of units to the left
1. Multiply the coefficients 2. Add the exponents

43. What number multiplied by itself is equal to 16? The answer is 4. Why?
1
Because 4 multiplied by itself equals 16.
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
perfect square

44. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
1. Divide the coefficients 2. Subtract the exponents
When moving the decimal point to the left (dividing by 10)
1

45. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
0
1. Multiply the coefficients 2. Add the exponents
decrease the value of the exponent by 1 (dividing by 10)
proper scientific

46. Indicates the number to be multiplied.
Moving the decimal point to the left
base
proper scientific
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

47. A very small number such as 0.000000674 can be written with scientific notation as
a fractional decimal
the radical sign with a little 3 that indicates the cube root:
6.74 x 10^-7
cubed

48. To multiply powers of 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.
10^1
1 divided by that number with a positive exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

49. Multiplying by 10
10^-2
10^-18
proper scientific
Moving the decimal point to the right

50. Negative cube roots are okay ... negative square roots are
10^-1
move the decimal point the same number of units to the left
Moving the decimal point to the left
Not