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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. = 0.1 - or 1 with the decimal point moved one place to the left.
0
10^-1
1. Multiply the coefficients 2. Add the exponents
negative number

2. Negative cube roots are okay ... negative square roots are
0
Not
1
6.74 x 10^-7

3. Any number with an exponent of 1 is equal to
one digit to the left of the decimal point
itself
change both terms in order to keep the value the same.
increase the power-of-10 exponent by the same number of units

4. Always 10 for scientific notation
10^2
squared
When moving the decimal point to the left (dividing by 10)
base

5. 0^5 =
1
When moving the decimal point to the left (dividing by 10)
0
coefficient

6. Indicates the number to be multiplied.
To multiply powers that have the same base:
base
change both terms in order to keep the value the same.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

7. When you change the position of the decimal point in a coefficient value
1
you have to adjust the value of the exponent in order avoid changing the actual value.
10^1
5

8. 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.
base
Are Equal
radical sign
Step 1. Divide the coefficients of the terms

9. The square of 3 is
1 divided by that number with a positive exponent
the radical sign with a little 3 that indicates the cube root:
0
9 (3^2 = 9)

10. To divide powers that have the same base:
When the exponent of a power-of-10 expression is a negative integer:
perfect square
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

11. A number - when multiplied by itself - is equal to a given number.
To multiply powers that have the same base:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
cubed
square root

12. A negative exponent does not mean the decimal value is negative. It means the decimal value is
The solution exists - but not in the real number system.
Are Equal
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
a fractional decimal

13. The cube root of zero is
proper scientific
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
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

14. Powers of ten can be added or subtracted only when their exponents
Are Equal
To multiply powers that have the same base:
2
5

15. What number multiplied by itself is equal to 16? The answer is 4. Why?
Subtract the exponent
exponent
Because 4 multiplied by itself equals 16.
radical sign

16. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
10^1
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

17. The square root of 9 is
3
Moving the decimal point to the left
10^-2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

18. 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
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
6.74 x 10^-7
1. Divide the coefficients 2. Subtract the exponents
adjust the value of the coefficient

19. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
Because 4 multiplied by itself equals 16.
Calculator square-root key
Moving the decimal point to the left

20. The decimal part
10^-2
9 (3^2 = 9)
coefficient
must be multiples of 3 or 0

21. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
0
1
2 x 10^9
decrease the value of the exponent by 1 (dividing by 10)

22. To add powers of ten:
Same base
Moving the decimal point to the right
Calculator square-root key
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

23. The cube root of a negative number is also a
2 x 10^9
increase the power-of-10 exponent by the same number of units
negative number
Calculator square-root key

24. = 0.01 - or 1 with the decimal point moved two places to the left.
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^-2
adjust the value of the coefficient
Not

25. A number is a second number which - when multiplied by itself three times - equals the original number.
1
Step 1. Divide the coefficients of the terms
Scientific notation
cube root

26.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
perfect square
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

27. 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
10^2
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
cube-root key

28. 1 to any power is equal to
1
10^-1
the radical sign with a little 3 that indicates the cube root:
change both terms in order to keep the value the same.

29. When you decrease the value of the power-of-10 exponent
10^-1
move the decimal point the same number of units to the right
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
3

30. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
increase the power-of-10 exponent by the same number of units

31. A very small number such as 0.000000674 can be written with scientific notation as
10^2
0
6.74 x 10^-7
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

32. 1 to any power is equal to
The solution exists - but not in the real number system.
cube root
1
Same base

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

34. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
10^-18
Scientific notation
Subtract the exponent
negative number

35. 100 - or 1 with the decimal point moved two places to the right
base
10^-1
10^2
0

36. Dividing by 10
cube root
the radical sign with a little 3 that indicates the cube root:
cube-root key
Moving the decimal point to the left

37. 3^0 =
1
1 divided by that number with a positive exponent
itself
one digit to the left of the decimal point

38. Any number with an exponent of 0 is equal to
1
Same base
squared
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

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

40. Numbers with exponents can be directly multiplied or divided only when they have the
base
Same base
9 (3^2 = 9)
you have to adjust the value of the exponent in order avoid changing the actual value.

41. For the 10
a fractional decimal
negative number
exponent
Engineering notation

42. When you move the decimal point in the coefficient to the right
Same base
2 x 10^9
decrease the power-of-10 exponent by the same number of units
itself

43. To multiply powers of ten:
Moving the decimal point to the left
Subtract the exponent
1. Multiply the coefficients 2. Add the exponents
cubed

44. Indicates the number of times the base is to be multiplied.
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
1. Divide the coefficients 2. Subtract the exponents
exponent

45. 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
1
5
same exponent
10^1

46. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
adjust the value of the coefficient
cube root
2 x 10^9

47. 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
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
change both terms in order to keep the value the same.
move the decimal point the same number of units to the right
0

48. Increase the value of the exponent by 1 (multiplying by 10)
To multiply powers that have the same base:
Scientific notation
Because 4 multiplied by itself equals 16.
When moving the decimal point to the left (dividing by 10)

49. A number with an exponent of 3 is often said to be
3
1 divided by that number with a positive exponent
cubed
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

50. 0 to any power is equal to
one digit to the left of the decimal point
0
the radical sign with a little 3 that indicates the cube root:
1