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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. The square root of zero is
same exponent
Same base
0
10^-18

2. Increase the value of the exponent by 1 (multiplying by 10)
exponent
When moving the decimal point to the left (dividing by 10)
3
0

3. 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
same exponent
Calculator square-root key
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

4. 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
1
you have to adjust the value of the exponent in order avoid changing the actual value.
square root
adjust the value of the coefficient

5. When you move the decimal point in the coefficient to the left
one digit to the left of the decimal point
proper scientific
1
increase the power-of-10 exponent by the same number of units

6.
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
move the decimal point the same number of units to the right
Moving the decimal point to the left
3

7. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
adjust the value of the coefficient
itself
10^2

8. Valid powers-of-10 for engineering notation
1. Divide the coefficients 2. Subtract the exponents
Step 1. Divide the coefficients of the terms
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
must be multiples of 3 or 0

9. An integer that is found by squaring another integer. You already know how to find the square root of 25 because it is a perfect square: 5 x 5 = 25 - or you could write it as 52 = 25. So 25 is a perfect square - and its square root is 5.
1 divided by that number with a positive exponent
Not
negative number
perfect square

10. The square root of 9 is
3
move the decimal point the same number of units to the left
To multiply powers that have the same base:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

11. 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
2 x 10^9
same exponent
10^-2
1. Divide the coefficients 2. Subtract the exponents

12. There are no special rules for adding and subtracting numbers that are written with exponents.
Moving the decimal point to the left
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
base

13. To divide powers of ten:
5
move the decimal point the same number of units to the right
1. Divide the coefficients 2. Subtract the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.

14. The cube root of a negative number is also a
1
negative number
Because 4 multiplied by itself equals 16.
Are Equal

15. Powers of ten can be added or subtracted only when their exponents
2 x 10^9
cubed
must be multiples of 3 or 0
Are Equal

16. = 0.01 - or 1 with the decimal point moved two places to the left.
When moving the decimal point to the left (dividing by 10)
itself
increase the power-of-10 exponent by the same number of units
10^-2

17. Numbers with exponents can be directly multiplied or divided only when they have the
Same base
5
move the decimal point the same number of units to the left
1

18. 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.
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
When the exponent of a power-of-10 expression is a negative integer:
itself
10^-18

19. Negative cube roots are okay ... negative square roots are
1
10^-2
Not
perfect square

20. Indicates the number to be multiplied.
base
Same base
6.74 x 10^-7
1 divided by that number with a positive exponent

21. Scientific notation requires there to be only
rewrite one of the terms so that the exponents are equal
Engineering notation
one digit to the left of the decimal point
radical sign

22. To multiply or divide exponent terms that do not have the same base:
10^-1
1
rewrite one of the terms so that the exponents are equal
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

23. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Not
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
2 x 10^9
move the decimal point the same number of units to the left

24. The decimal part
coefficient
change both terms in order to keep the value the same.
0
move the decimal point the same number of units to the right

25. Indicates the number of times the base is to be multiplied.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
proper scientific
exponent
Step 1. Divide the coefficients of the terms

26. To subtract powers of ten:
10^2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
When moving the decimal point to the left (dividing by 10)
radical sign

27. Represents 1 preceded by 17 zeros and a decimal point.
Same base
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
10^-18

28. Step 1: Add the exponents Step 2: Use the common base
Same base
Moving the decimal point to the left
To multiply powers that have the same base:
square root

29. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
increase the power-of-10 exponent by the same number of units
must be multiples of 3 or 0
0

30. 5^1 =
5
exponent
rewrite one of the terms so that the exponents are equal
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

31. 1 to any power is equal to
adjust the value of the coefficient
itself
exponent
1

32. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
0
increase the power-of-10 exponent by the same number of units
10^-1

33. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Because 4 multiplied by itself equals 16.
1
Subtract the exponent

34. Any number with an exponent of 0 is equal to
1
you have to adjust the value of the exponent in order avoid changing the actual value.
base
same exponent

35. 0^5 =
10^-2
exponent
3
0

36. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
1. Divide the coefficients 2. Subtract the exponents
Same base
Not

37. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
2 x 10^9
To multiply powers that have the same base:
decrease the power-of-10 exponent by the same number of units
proper scientific

38. What number multiplied by itself is equal to 16? The answer is 4. Why?
rewrite one of the terms so that the exponents are equal
To multiply powers that have the same base:
1
Because 4 multiplied by itself equals 16.

39. 1 to any power is equal to
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1
a fractional decimal
0

40. Dividing by 10
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
cubed
decrease the power-of-10 exponent by the same number of units
Moving the decimal point to the left

41. 1^4 =
1
decrease the value of the exponent by 1 (dividing by 10)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
3

42. 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.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1
Engineering notation
negative number

43. When you change the position of the decimal point in a coefficient value
6.74 x 10^-7
you have to adjust the value of the exponent in order avoid changing the actual value.
1
radical sign

44. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
To multiply powers that have the same base:
base
0

45. Valid powers of 10 for engineering notation are:
must be multiples of 3 or 0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^-2
3

46. The cube root of zero is
exponent
proper scientific
1. Divide the coefficients 2. Subtract the exponents
0

47. The square of 3 is
Scientific notation
squared
9 (3^2 = 9)
Calculator square-root key

48. A number with an exponent of 3 is often said to be
cubed
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.
cube root
Moving the decimal point to the right

49. = 0.1 - or 1 with the decimal point moved one place to the left.
base
10^-1
When moving the decimal point to the left (dividing by 10)
1

50. 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
square root
cube-root key
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^1