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. Indicates the number to be multiplied.
radical sign
base
one digit to the left of the decimal point
Engineering notation

2. When you move the decimal point in the coefficient to the left
rewrite one of the terms so that the exponents are equal
increase the power-of-10 exponent by the same number of units
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1. Multiply the coefficients 2. Add the exponents

3. When you change the position of the decimal point in a coefficient value
cubed
When the exponent of a power-of-10 expression is a negative integer:
you have to adjust the value of the exponent in order avoid changing the actual value.
1. Multiply the coefficients 2. Add the exponents

4. 0^5 =
To multiply powers that have the same base:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
base
0

5. Negative cube roots are okay ... negative square roots are
Not
increase the power-of-10 exponent by the same number of units
one digit to the left of the decimal point
The solution exists - but not in the real number system.

6. 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
cubed
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

7. The symbol for the cube root of a number is
Because 4 multiplied by itself equals 16.
change both terms in order to keep the value the same.
9 (3^2 = 9)
the radical sign with a little 3 that indicates the cube root:

8. 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
When the exponent of a power-of-10 expression is a negative integer:
10^-2
To multiply powers that have the same base:

9. There are no special rules for adding and subtracting numbers that are written with exponents.
Calculator square-root key
move the decimal point the same number of units to the left
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
coefficient

10. Numbers with exponents can be directly multiplied or divided only when they have the
10^-1
coefficient
Same base
To multiply powers that have the same base:

11. 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
decrease the value of the exponent by 1 (dividing by 10)
To multiply powers that have the same base:
cube root

12. 10 - or 1 with the decimal point moved one place to the right
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^1
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

13. 1^4 =
Step 1. Divide the coefficients of the terms
1
move the decimal point the same number of units to the left
To multiply powers that have the same base:

14. The square root of 9 is
3
Are Equal
decrease the value of the exponent by 1 (dividing by 10)
change both terms in order to keep the value the same.

15. Dividing by 10
itself
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Moving the decimal point to the left
decrease the value of the exponent by 1 (dividing by 10)

16. To find the square root of any number - simply key in the number (the radicand) and press the
coefficient
you have to adjust the value of the exponent in order avoid changing the actual value.
10^2
Calculator square-root key

17. Scientific notation requires there to be only
9 (3^2 = 9)
Moving the decimal point to the right
cube-root key
one digit to the left of the decimal point

18. = 0.01 - or 1 with the decimal point moved two places to the left.
10^1
10^-2
Subtract the exponent
the radical sign with a little 3 that indicates the cube root:

19. 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 divided by that number with a positive exponent
When the exponent of a power-of-10 expression is a negative integer:
you have to adjust the value of the exponent in order avoid changing the actual value.
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

20. A very small number such as 0.000000674 can be written with scientific notation as
1
1
6.74 x 10^-7
Because 4 multiplied by itself equals 16.

21. Valid powers-of-10 for engineering notation
base
10^-1
must be multiples of 3 or 0
1

22. 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.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Engineering notation
3

23. To add powers of ten:
same exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0
move the decimal point the same number of units to the left

24. To subtract powers of ten:
5
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
coefficient
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.

25. 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
Are Equal
exponent
Subtract the exponent

26. For the 10
radical sign
cubed
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
exponent

27. 1 to any power is equal to
9 (3^2 = 9)
1
1. Divide the coefficients 2. Subtract the exponents
Same base

28. Represents 1 preceded by 17 zeros and a decimal point.
5
perfect square
10^-18
Calculator square-root key

29. 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
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^1
adjust the value of the coefficient

30. When moving the decimal point to the right (multiplying by 10)
2
decrease the value of the exponent by 1 (dividing by 10)
10^-2
cube root

31. A negative exponent does not mean the decimal value is negative. It means the decimal value is
coefficient
1
decrease the power-of-10 exponent by the same number of units
a fractional decimal

32. The cube root of zero is
0
1
coefficient
10^1

33. 1 to any power is equal to
Moving the decimal point to the right
Because 4 multiplied by itself equals 16.
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.
1

34. Valid powers of 10 for engineering notation are:
Scientific notation
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
0

35. When you move the decimal point in the coefficient to the right
Moving the decimal point to the left
coefficient
decrease the power-of-10 exponent by the same number of units
5

36. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
10^2
squared
must be multiples of 3 or 0

37. To divide powers of 10:
0
Step 1. Divide the coefficients of the terms
move the decimal point the same number of units to the right
1

38. 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
2 x 10^9
base

39. To multiply or divide exponent terms that do not have the same base:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Divide the coefficients of the terms
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^1

40. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Not
2 x 10^9

41. 100 - or 1 with the decimal point moved two places to the right
10^-1
10^2
1 divided by that number with a positive exponent
cube-root key

42. A number with an exponent of 3 is often said to be
cubed
decrease the power-of-10 exponent by the same number of units
move the decimal point the same number of units to the right
change both terms in order to keep the value the same.

43. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
move the decimal point the same number of units to the right

44. Don't bother trying to find the square root of a negative number.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
itself
The solution exists - but not in the real number system.
Same base

45. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
When moving the decimal point to the left (dividing by 10)
2

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.
10^-1
radical sign
2 x 10^9
Moving the decimal point to the left

47. = 0.1 - or 1 with the decimal point moved one place to the left.
10^1
When the exponent of a power-of-10 expression is a negative integer:
0
10^-1

48. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
0
Scientific notation
5

49. When the exponents are not the same
1
rewrite one of the terms so that the exponents are equal
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
Moving the decimal point to the right

50. A number - when multiplied by itself - is equal to a given number.
decrease the value of the exponent by 1 (dividing by 10)
rewrite one of the terms so that the exponents are equal
increase the power-of-10 exponent by the same number of units
square root