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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. A number with an exponent of 3 is often said to be
Moving the decimal point to the left
the radical sign with a little 3 that indicates the cube root:
10^1
cubed

2. 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.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
itself
10^1

3. 0^5 =
0
Same base
The solution exists - but not in the real number system.
same exponent

4. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
decrease the value of the exponent by 1 (dividing by 10)
Moving the decimal point to the left
Calculator square-root key

5. A number with an exponent of 2 is often said to be
decrease the value of the exponent by 1 (dividing by 10)
Moving the decimal point to the right
squared
increase the power-of-10 exponent by the same number of units

6. To multiply powers of ten:
decrease the power-of-10 exponent by the same number of units
1. Multiply the coefficients 2. Add the exponents
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

7. To divide powers that have the same base:
Not
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^-18
perfect square

8. Dividing by 10
Moving the decimal point to the left
0
1
cubed

9. = 0.01 - or 1 with the decimal point moved two places to the left.
decrease the value of the exponent by 1 (dividing by 10)
10^1
Moving the decimal point to the left
10^-2

10. When you move the decimal point in the coefficient to the right
1 divided by that number with a positive exponent
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Same base
decrease the power-of-10 exponent by the same number of units

11. 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
1
Subtract the exponent
increase the power-of-10 exponent by the same number of units
change both terms in order to keep the value the same.

12. = 0.1 - or 1 with the decimal point moved one place to the left.
Calculator square-root key
10^-2
10^-1
a fractional decimal

13. A very small number such as 0.000000674 can be written with scientific notation as
radical sign
cube root
move the decimal point the same number of units to the right
6.74 x 10^-7

14. To divide powers of ten:
The solution exists - but not in the real number system.
1. Divide the coefficients 2. Subtract the exponents
coefficient
cube-root key

15. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
1
proper scientific
base
2 x 10^9

16. 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.
move the decimal point the same number of units to the right
cubed
9 (3^2 = 9)

17. 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
Scientific notation
cube-root key
increase the power-of-10 exponent by the same number of units
To multiply powers that have the same base:

18. 100 - or 1 with the decimal point moved two places to the right
Moving the decimal point to the left
Same 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
10^2

19. Always 10 for scientific notation
cubed
base
square root
change both terms in order to keep the value the same.

20. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
1. Divide the coefficients 2. Subtract the exponents
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 divided by that number with a positive exponent

21.
exponent
Are Equal
When moving the decimal point to the left (dividing by 10)
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

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
0
Moving the decimal point to the left
exponent

23. Indicates the number to be multiplied.
1
base
one digit to the left of the decimal point
2 x 10^9

24. To divide powers of 10:
square root
Step 1. Divide the coefficients of the terms
one digit to the left of the decimal point
base

25. The cube root of zero is
10^-2
0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1

26. 5^1 =
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
5
increase the power-of-10 exponent by the same number of units
9 (3^2 = 9)

27. To add powers of ten:
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. Divide the coefficients 2. Subtract the exponents
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
5

28. Indicates the number of times the base is to be multiplied.
When the exponent of a power-of-10 expression is a negative integer:
change both terms in order to keep the value the same.
Step 1. Divide the coefficients of the terms
exponent

29. When you decrease the value of the power-of-10 exponent
1
When moving the decimal point to the left (dividing by 10)
move the decimal point the same number of units to the right
1

30. Multiplying by 10
Moving the decimal point to the right
square root
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
must be multiples of 3 or 0

31. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
decrease the power-of-10 exponent by the same number of units
2 x 10^9
10^2
1

32. Don't bother trying to find the square root of a negative number.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
itself
1 divided by that number with a positive exponent
The solution exists - but not in the real number system.

33. Negative cube roots are okay ... negative square roots are
Not
5
increase the power-of-10 exponent by the same number of units
rewrite one of the terms so that the exponents are equal

34. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Calculator square-root key
3
Are Equal

35. 1 to any power is equal to
Same base
perfect square
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

36. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
1 divided by that number with a positive exponent
Scientific notation
When moving the decimal point to the left (dividing by 10)

37. 10 - or 1 with the decimal point moved one place to the right
Are Equal
1. Multiply the coefficients 2. Add the exponents
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^1

38. 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
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
move the decimal point the same number of units to the right
9 (3^2 = 9)

39. The square root of 9 is
3
0
1
Not

40. What number multiplied by itself is equal to 16? The answer is 4. Why?
base
The solution exists - but not in the real number system.
Not
Because 4 multiplied by itself equals 16.

41. The decimal part
coefficient
proper scientific
Subtract the exponent
exponent

42. 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.
adjust the value of the coefficient
exponent
cube-root key
When the exponent of a power-of-10 expression is a negative integer:

43. 3^0 =
you have to adjust the value of the exponent in order avoid changing the actual value.
1
5
square root

44. For the 10
negative number
move the decimal point the same number of units to the right
2
exponent

45. When you move the decimal point in the coefficient to the left
0
increase the power-of-10 exponent by the same number of units
decrease the power-of-10 exponent by the same number of units
The solution exists - but not in the real number system.

46. To multiply or divide exponent terms that do not have the same base:
Moving the decimal point to the right
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
squared
base

47. 1 to any power is equal to
10^1
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.
exponent

48. The square of 3 is
exponent
Calculator square-root key
0
9 (3^2 = 9)

49. When you increase the value of the power-of-10 exponent
1. Divide the coefficients 2. Subtract the exponents
decrease the power-of-10 exponent by the same number of units
move the decimal point the same number of units to the right
move the decimal point the same number of units to the left

50. 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
Moving the decimal point to the right
The solution exists - but not in the real number system.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.