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 decimal part
coefficient
Not
adjust the value of the coefficient
Moving the decimal point to the left

2. A number is a second number which - when multiplied by itself three times - equals the original number.
1
1 divided by that number with a positive exponent
10^-1
cube root

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

4. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
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
cubed

5. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the right
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Calculator square-root key
move the decimal point the same number of units to the left

6. A number - when multiplied by itself - is equal to a given 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
cube-root key
Moving the decimal point to the left
square root

7. 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.
Subtract the exponent
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
0

8. Powers of ten can be added or subtracted only when their exponents
1
To multiply powers that have the same base:
Are Equal
rewrite one of the terms so that the exponents are equal

9. Dividing by 10
Step 1. Divide the coefficients of the terms
Moving the decimal point to the left
1. Divide the coefficients 2. Subtract the exponents
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

10. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Scientific notation
same exponent
Moving the decimal point to the right

11. To add or subtract numbers written with exponents:
9 (3^2 = 9)
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
10^-2
cube root

12. 0^5 =
negative number
0
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

13. 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
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.
squared
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

14. To divide powers of 10:
cubed
squared
Step 1. Divide the coefficients of the terms
base

15. 1^4 =
1
When moving the decimal point to the left (dividing by 10)
radical sign
0

16. Any number with a negative exponent is equal to
coefficient
When the exponent of a power-of-10 expression is a negative integer:
1 divided by that number with a positive exponent
0

17.
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
0
you have to adjust the value of the exponent in order avoid changing the actual value.
Because 4 multiplied by itself equals 16.

18. To find the square root of any number - simply key in the number (the radicand) and press the
Are Equal
Calculator square-root key
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
5

19. To add powers of ten:
10^2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
The solution exists - but not in the real number system.
5

20. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
Moving the decimal point to the right
2 x 10^9
3

21. 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.
9 (3^2 = 9)
Moving the decimal point to the left
change both terms in order to keep the value the same.

22. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
negative number
you have to adjust the value of the exponent in order avoid changing the actual value.
2 x 10^9
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

23. The square root of zero is
the radical sign with a little 3 that indicates the cube root:
1
0
10^1

24. When you move the decimal point in the coefficient to the right
decrease the power-of-10 exponent by the same number of units
To multiply powers that have the same base:
perfect square
1

25. What number multiplied by itself is equal to 16? The answer is 4. Why?
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
Step 1. Divide the coefficients of the terms
Because 4 multiplied by itself equals 16.

26. 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
Subtract the exponent
2
move the decimal point the same number of units to the left

27. There are no special rules for adding and subtracting numbers that are written with exponents.
move the decimal point the same number of units to the right
exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
When moving the decimal point to the left (dividing by 10)

28. Increase the value of the exponent by 1 (multiplying by 10)
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
When moving the decimal point to the left (dividing by 10)
move the decimal point the same number of units to the right
radical sign

29. When you change the position of the decimal point in a coefficient value
you have to adjust the value of the exponent in order avoid changing the actual value.
10^-1
cube root
increase the power-of-10 exponent by the same number of units

30. For the 10
exponent
the radical sign with a little 3 that indicates the cube root:
increase the power-of-10 exponent by the same number of units
one digit to the left of the decimal point

31. 10 - or 1 with the decimal point moved one place to the right
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^1
decrease the power-of-10 exponent by the same number of units
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

32. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
10^-18
Subtract the exponent
you have to adjust the value of the exponent in order avoid changing the actual value.
itself

33. Don't bother trying to find the square root of a negative number.
10^-2
Because 4 multiplied by itself equals 16.
1. Multiply the coefficients 2. Add the exponents
The solution exists - but not in the real number system.

34. 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.
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 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
move the decimal point the same number of units to the right

35. 1 to any power is equal to
Scientific notation
one digit to the left of the decimal point
9 (3^2 = 9)
1

36. When moving the decimal point to the right (multiplying by 10)
itself
decrease the value of the exponent by 1 (dividing by 10)
5
square root

37. Numbers with exponents can be directly multiplied or divided only when they have the
move the decimal point the same number of units to the right
square root
5
Same base

38. 100 - or 1 with the decimal point moved two places to the right
decrease the power-of-10 exponent by the same number of units
1. Divide the coefficients 2. Subtract the exponents
10^2
same exponent

39. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
0
1. Multiply the coefficients 2. Add the exponents
Not

40. To divide powers of ten:
Same base
1. Divide the coefficients 2. Subtract the exponents
adjust the value of the coefficient
increase the power-of-10 exponent by the same number of units

41. When you move the decimal point in the coefficient to the left
0
same exponent
Engineering notation
increase the power-of-10 exponent by the same number of units

42. 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
coefficient
adjust the value of the coefficient
cube-root key
Engineering notation

43. 1 to any power is equal to
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^-2
decrease the value of the exponent by 1 (dividing by 10)
1

44. The square root of 9 is
3
increase the power-of-10 exponent by the same number of units
10^-1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

45. Any number with an exponent of 1 is equal to
decrease the value of the exponent by 1 (dividing by 10)
move the decimal point the same number of units to the left
itself
When moving the decimal point to the left (dividing by 10)

46. To divide powers that have the same base:
base
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
a fractional decimal
9 (3^2 = 9)

47. The symbol for the cube root of a number is
proper scientific
same exponent
base
the radical sign with a little 3 that indicates the cube root:

48. 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.
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
radical sign
Scientific notation
3

49. = 0.1 - or 1 with the decimal point moved one place to the left.
10^1
10^-1
Scientific notation
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

50. Any number with an exponent of 0 is equal to
1
Because 4 multiplied by itself equals 16.
itself
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.