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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. To multiply powers of ten:
you have to adjust the value of the exponent in order avoid changing the actual value.
Same base
squared
1. Multiply the coefficients 2. Add the exponents

2. The symbol for the cube root of a number is
1
the radical sign with a little 3 that indicates the cube root:
negative number
base

3. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
decrease the power-of-10 exponent by the same number of units
Moving the decimal point to the left
10^-1

4. Negative cube roots are okay ... negative square roots are
2 x 10^9
Not
exponent
move the decimal point the same number of units to the left

5. 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.
move the decimal point the same number of units to the right
cube-root key
adjust the value of the coefficient
When the exponent of a power-of-10 expression is a negative integer:

6. The cube root of zero is
adjust the value of the coefficient
The solution exists - but not in the real number system.
3
0

7. Valid powers of 10 for engineering notation are:
cubed
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
one digit to the left of the decimal point
coefficient

8. The square of 3 is
5
The solution exists - but not in the real number system.
decrease the power-of-10 exponent by the same number of units
9 (3^2 = 9)

9. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
cubed
Not
negative number

10. What number multiplied by itself is equal to 16? The answer is 4. Why?
0
Because 4 multiplied by itself equals 16.
2
Same base

11. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Moving the decimal point to the right
move the decimal point the same number of units to the right
2 x 10^9
exponent

12. A number with an exponent of 2 is often said to be
squared
1. Divide the coefficients 2. Subtract the exponents
10^-18
9 (3^2 = 9)

13. 3^0 =
itself
1
2
cube-root key

14. Indicates the number of times the base is to be multiplied.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
decrease the power-of-10 exponent by the same number of units
exponent
2

15. 1 to any power is equal to
Moving the decimal point to the right
1
1. Multiply the coefficients 2. Add the exponents
0

16. Step 1: Add the exponents Step 2: Use the common base
the radical sign with a little 3 that indicates the cube root:
9 (3^2 = 9)
To multiply powers that have the same base:
one digit to the left of the decimal point

17. 100 - or 1 with the decimal point moved two places to the right
10^2
10^-2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
base

18. 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.
negative number
radical sign
one digit to the left of the decimal point
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

19. 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
1
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

20. A number with an exponent of 3 is often said to be
radical sign
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
cubed
change both terms in order to keep the value the same.

21. Any number with a negative exponent is equal to
increase the power-of-10 exponent by the same number of units
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
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

22. 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.
Engineering 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.
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
cubed

23. To divide powers that have the same base:
same exponent
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
When moving the decimal point to the left (dividing 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

24. To add powers of ten:
2 x 10^9
rewrite one of the terms so that the exponents are equal
1. Multiply the coefficients 2. Add the exponents
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

25. Increase the value of the exponent by 1 (multiplying by 10)
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
change both terms in order to keep the value the same.
When moving the decimal point to the left (dividing by 10)
1

26. A number - when multiplied by itself - is equal to a given number.
rewrite one of the terms so that the exponents are equal
radical sign
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
square root

27. A number is a second number which - when multiplied by itself three times - equals the original number.
same exponent
cubed
rewrite one of the terms so that the exponents are equal
cube root

28. 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
rewrite one of the terms so that the exponents are equal
0
adjust the value of the coefficient
Scientific notation

29. 10 - or 1 with the decimal point moved one place to the right
1
decrease the value of the exponent by 1 (dividing by 10)
10^1
1

30. Powers of ten can be added or subtracted only when their exponents
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
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Are Equal

31. Represents 1 preceded by 17 zeros and a decimal point.
must be multiples of 3 or 0
10^-18
change both terms in order to keep the value the same.
5

32. When you move the decimal point in the coefficient to the left
9 (3^2 = 9)
1
1
increase the power-of-10 exponent by the same number of units

33. There are no special rules for adding and subtracting numbers that are written with exponents.
cube-root key
perfect square
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1

34. To multiply or divide exponent terms that do not have the same base:
one digit to the left of the decimal point
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Same base
exponent

35. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
itself
10^-1
Same base

36. 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
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
Scientific notation

37. Multiplying by 10
10^-1
Moving the decimal point to the right
Moving the decimal point to the left
To multiply powers that have the same base:

38. Scientific notation requires there to be only
same exponent
one digit to the left of the decimal point
0
must be multiples of 3 or 0

39. 1^4 =
1
move the decimal point the same number of units to the right
rewrite one of the terms so that the exponents are equal
9 (3^2 = 9)

40. The cube root of a negative number is also a
decrease the power-of-10 exponent by the same number of units
3
negative number
square root

41. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Engineering notation
cube-root key
proper scientific
change both terms in order to keep the value the same.

42. Any number with an exponent of 0 is equal to
1. Divide the coefficients 2. Subtract the exponents
exponent
Not
1

43. To multiply powers of 10:
itself
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.
1. Divide the coefficients 2. Subtract the 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

44. To divide powers of 10:
Calculator square-root key
base
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

45. 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
10^1
a fractional decimal
one digit to the left of the decimal point

46. = 0.01 - or 1 with the decimal point moved two places to the left.
base
base
10^-2
itself

47. 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.
Scientific notation
same exponent
move the decimal point the same number of units to the right

48. To subtract powers of ten:
10^-2
Calculator square-root key
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1. Multiply the coefficients 2. Add the exponents

49. To divide powers of ten:
exponent
1. Divide the coefficients 2. Subtract the exponents
adjust the value of the coefficient
cubed

50. The square root of zero is
decrease the power-of-10 exponent by the same number of units
Are Equal
0
10^-2