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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. 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
Calculator square-root key
1 divided by that number with a positive exponent

2. Dividing by 10
cube-root key
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.
itself
Moving the decimal point to the left

3. To subtract powers of ten:
1
a fractional decimal
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Scientific notation

4. Indicates the number to be multiplied.
base
cube-root key
10^-2
10^-18

5. Multiplying by 10
Moving the decimal point to the right
2
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

6. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
exponent
1
proper scientific
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

7. 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
same exponent
Moving the decimal point to the right
adjust the value of the coefficient

8. There are no special rules for adding and subtracting numbers that are written with exponents.
Not
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Scientific notation
you have to adjust the value of the exponent in order avoid changing the actual value.

9. To add or subtract numbers written with exponents:
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
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Engineering notation
move the decimal point the same number of units to the right

10. 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.
Scientific notation
decrease the power-of-10 exponent by the same number of units
2

11. A number is a second number which - when multiplied by itself three times - equals the original number.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
cube root
square root
base

12. 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.
10^1
1 divided by that number with a positive exponent
0
When the exponent of a power-of-10 expression is a negative integer:

13. The square root of 9 is
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
square root
0
3

14. 0 to any power is equal to
Same base
The solution exists - but not in the real number system.
cube root
0

15. A very small number such as 0.000000674 can be written with scientific notation as
1
1
base
6.74 x 10^-7

16. The square root of zero is
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0
6.74 x 10^-7
Moving the decimal point to the right

17. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1. Divide the coefficients 2. Subtract the exponents
0
2
Calculator square-root key

18. The square of 3 is
must be multiples of 3 or 0
a fractional decimal
2 x 10^9
9 (3^2 = 9)

19. 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.
itself
decrease the power-of-10 exponent by the same number of units
1 divided by that number with a positive exponent

20.
10^-18
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
the radical sign with a little 3 that indicates the cube root:
move the decimal point the same number of units to the right

21. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
Engineering notation
one digit to the left of the decimal point
Moving the decimal point to the left

22. A number with an exponent of 3 is often said to be
cubed
Not
10^-2
0

23. To multiply powers of ten:
you have to adjust the value of the exponent in order avoid changing the actual value.
1. Multiply the coefficients 2. Add the exponents
cube root
Not

24. To find the square root of any number - simply key in the number (the radicand) and press the
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Calculator square-root key
2
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

25. 10 - or 1 with the decimal point moved one place to the right
1
10^1
Engineering notation
same exponent

26. Valid powers-of-10 for engineering notation
1
must be multiples of 3 or 0
1. Divide the coefficients 2. Subtract the exponents
cube root

27. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
same exponent
Calculator square-root key
Same base

28. Always 10 for scientific notation
Not
base
1
must be multiples of 3 or 0

29. The cube root of zero is
0
1. Divide the coefficients 2. Subtract the exponents
To multiply powers that have the same base:
base

30. A number - when multiplied by itself - is equal to a given number.
square root
1. Multiply the coefficients 2. Add the exponents
0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

31. A negative exponent does not mean the decimal value is negative. It means the decimal value is
move the decimal point the same number of units to the left
move the decimal point the same number of units to the right
decrease the value of the exponent by 1 (dividing by 10)
a fractional decimal

32. Powers of ten can be added or subtracted only when their exponents
exponent
base
Are Equal
itself

33. 1 to any power is equal to
Calculator square-root key
0
Same base
1

34. 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
perfect square
must be multiples of 3 or 0
Moving the decimal point to the left

35. The decimal part
cubed
negative number
coefficient
decrease the value of the exponent by 1 (dividing by 10)

36. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.
proper scientific
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

37. For the 10
Calculator square-root key
exponent
base
To multiply powers that have the same base:

38. 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.
10^-18
Engineering notation
rewrite one of the terms so that the exponents are equal
1

39. 0^5 =
10^-18
coefficient
0
Subtract the exponent

40. 100 - or 1 with the decimal point moved two places to the right
9 (3^2 = 9)
10^2
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
0

41. To add powers of ten:
square root
must be multiples of 3 or 0
itself
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

42. 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.
same exponent
Scientific notation
5
When moving the decimal point to the left (dividing by 10)

43. Don't bother trying to find the square root of a negative number.
Subtract the exponent
5
The solution exists - but not in the real number system.
10^2

44. = 0.01 - or 1 with the decimal point moved two places to the left.
1
Same base
10^-2
coefficient

45. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
squared
1
10^-18

46. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
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
increase the power-of-10 exponent by the same number of units

47. When you increase the value of the power-of-10 exponent
cube root
perfect square
move the decimal point the same number of units to the left
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

48. 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 4 multiplied by itself equals 16.
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
0
increase the power-of-10 exponent by the same number of units

49. Represents 1 preceded by 17 zeros and a decimal point.
5
10^-18
10^1
square root

50. 3^0 =
10^1
1
3
10^-1