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CLEP General Mathematics: Powers Exponents And Roots

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
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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. 0^5 =
0
1. Multiply the coefficients 2. Add the 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

2. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
0
5
itself

3. There are no special rules for adding and subtracting numbers that are written with exponents.
The solution exists - but not in the real number system.
9 (3^2 = 9)
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
exponent

4. When the exponents are not the same
proper scientific
rewrite one of the terms so that the exponents are equal
move the decimal point the same number of units to the right
negative number

5. Any number with an exponent of 1 is equal to
base
itself
Subtract the exponent
1. Multiply the coefficients 2. Add the exponents

6. The decimal part
Same base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
cubed
coefficient

7. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
perfect square
base
2 x 10^9
3

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

9. 3^0 =
itself
the radical sign with a little 3 that indicates the cube root:
1
proper scientific

10. When you decrease the value of the power-of-10 exponent
you have to adjust the value of the exponent in order avoid changing the actual value.
1
10^1
move the decimal point the same number of units to the right

11. The square root of zero is
0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Calculator square-root key
2 x 10^9

12. Multiplying by 10
same exponent
a fractional decimal
Step 1. Divide the coefficients of the terms
Moving the decimal point to the right

13. 100 - or 1 with the decimal point moved two places to the right
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
Engineering notation
To multiply powers that have the same base:
10^2

14. 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
base
9 (3^2 = 9)
same exponent
a fractional decimal

15. The symbol for the cube root of a number is
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
the radical sign with a little 3 that indicates the cube root:
When the exponent of a power-of-10 expression is a negative integer:
0

16. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
same exponent
2 x 10^9
1. Divide the coefficients 2. Subtract the exponents

17. To divide powers of 10:
Step 1. Divide the coefficients of the terms
cubed
When the exponent of a power-of-10 expression is a negative integer:
change both terms in order to keep the value the same.

18. 10 - or 1 with the decimal point moved one place to the right
10^-2
10^1
base
adjust the value of the coefficient

19. Indicates the number of times the base is to be multiplied.
exponent
decrease the power-of-10 exponent by the same number of units
change both terms in order to keep the value the same.
adjust the value of the coefficient

20. 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.
increase the power-of-10 exponent by the same number of units
3
radical sign
decrease the power-of-10 exponent by the same number of units

21. 1 to any power is equal to
10^-1
radical sign
1
Moving the decimal point to the left

22. Numbers with exponents can be directly multiplied or divided only when they have the
1
10^2
Same base
cube root

23. Any number with a negative exponent is equal to
Not
1 divided by that number with a positive exponent
6.74 x 10^-7
Moving the decimal point to the right

24. Negative cube roots are okay ... negative square roots are
0
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.
Not
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

25. 1^4 =
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
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1 divided by that number with a positive exponent

26. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
To multiply powers that have the same base:
proper scientific
The solution exists - but not in the real number system.
exponent

27.
move the decimal point the same number of units to the left
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
5
1 divided by that number with a positive exponent

28. 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
one digit to the left of the decimal point
cubed
Because 4 multiplied by itself equals 16.
change both terms in order to keep the value the same.

29. The square root of 9 is
base
3
exponent
you have to adjust the value of the exponent in order avoid changing the actual value.

30. What number multiplied by itself is equal to 16? The answer is 4. Why?
Moving the decimal point to the left
Because 4 multiplied by itself equals 16.
The solution exists - but not in the real number system.
0

31. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
base
coefficient
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

32. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
10^-2
Step 1. Divide the coefficients of the terms
Calculator square-root key

33. To divide powers that have the same base:
cube root
a fractional decimal
Subtract the exponent
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

34. Always 10 for scientific notation
Because 4 multiplied by itself equals 16.
base
Engineering notation
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

35. Valid powers of 10 for engineering notation are:
0
one digit to the left of the decimal point
Same base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

36. Increase the value of the exponent by 1 (multiplying by 10)
coefficient
When moving the decimal point to the left (dividing by 10)
exponent
10^-1

37. Powers of ten can be added or subtracted only when their exponents
perfect square
Are Equal
To multiply powers that have the same base:
0

38. The cube root of zero is
rewrite one of the terms so that the exponents are equal
0
10^-18
negative number

39. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
square root
1
Moving the decimal point to the right

40. = 0.1 - or 1 with the decimal point moved one place to the left.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Calculator square-root key
10^-1
Engineering notation

41. A number with an exponent of 2 is often said to be
10^-1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
squared
you have to adjust the value of the exponent in order avoid changing the actual value.

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

43. To divide powers of ten:
10^2
10^-1
1. Divide the coefficients 2. Subtract the exponents
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

44. A number - when multiplied by itself - is equal to a given number.
the radical sign with a little 3 that indicates the cube root:
square root
adjust the value of the coefficient
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

45. A number with an exponent of 3 is often said to be
1
exponent
cubed
6.74 x 10^-7

46. When you increase the value of the power-of-10 exponent
5
1. Multiply the coefficients 2. Add the exponents
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
move the decimal point the same number of units to the left

47. The cube root of a negative number is also a
negative number
2 x 10^9
10^-2
base

48. To subtract powers of ten:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
10^-1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

49. To add powers of ten:
Moving the decimal point to the right
coefficient
base
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

50. 1 to any power is equal to
1 divided by that number with a positive exponent
6.74 x 10^-7
1
adjust the value of the coefficient