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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 of 3 is
Step 1. Divide the coefficients of the terms
1
1. Multiply the coefficients 2. Add the exponents
9 (3^2 = 9)

2. To multiply or divide exponent terms that do not have the same base:
5
change both terms in order to keep the value the same.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
exponent

3. To add or subtract numbers written with exponents:
cubed
the radical sign with a little 3 that indicates the cube root:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
must be multiples of 3 or 0

4. The symbol for the cube root of a number is
1 divided by that number with a positive exponent
Not
change both terms in order to keep the value the same.
the radical sign with a little 3 that indicates the cube root:

5. The cube root of zero is
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
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
0

6. What number multiplied by itself is equal to 16? The answer is 4. Why?
a fractional decimal
1 divided by that number with a positive exponent
exponent
Because 4 multiplied by itself equals 16.

7. The cube root of a negative number is also a
1 divided by that number with a positive exponent
negative number
cube-root key
Not

8. 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
cube-root key
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
adjust the value of the coefficient
1

9. 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 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 moving the decimal point to the left (dividing by 10)
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.

10. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Because 4 multiplied by itself equals 16.
adjust the value of the coefficient
base
Subtract the exponent

11. To subtract powers of ten:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
decrease the value of the exponent by 1 (dividing by 10)
When moving the decimal point to the left (dividing by 10)
squared

12. Any number with an exponent of 1 is equal to
1
radical sign
itself
Moving the decimal point to the right

13. Powers of ten can be added or subtracted only when their exponents
Moving the decimal point to the left
change both terms in order to keep the value the same.
adjust the value of the coefficient
Are Equal

14. Negative cube roots are okay ... negative square roots are
10^-1
Not
Are Equal
must be multiples of 3 or 0

15. 10 - or 1 with the decimal point moved one place to the right
10^1
you have to adjust the value of the exponent in order avoid changing the actual value.
exponent
proper scientific

16. Indicates the number of times the base is to be multiplied.
exponent
cube-root key
decrease the value of the exponent by 1 (dividing by 10)
proper scientific

17.
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
change both terms in order to keep the value the same.
move the decimal point the same number of units to the right
2

18. A number with an exponent of 3 is often said to be
1
rewrite one of the terms so that the exponents are equal
3
cubed

19. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
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
squared
Because 4 multiplied by itself equals 16.
proper scientific

20. Numbers with exponents can be directly multiplied or divided only when they have the
you have to adjust the value of the exponent in order avoid changing the actual value.
Same base
Because 4 multiplied by itself equals 16.
3

21. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
0
Moving the decimal point to the left
2
10^-1

22. Increase the value of the exponent by 1 (multiplying by 10)
1
When moving the decimal point to the left (dividing by 10)
change both terms in order to keep the value the same.
a fractional decimal

23. To add powers of ten:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Scientific notation
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

24. To multiply powers of 10:
3
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
base

25. Dividing by 10
1
Moving the decimal point to the left
negative number
proper scientific

26. Scientific notation requires there to be only
change both terms in order to keep the value the same.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1
one digit to the left of the decimal point

27. 1 to any power is equal to
coefficient
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
0
1

28. To multiply powers of ten:
0
same exponent
rewrite one of the terms so that the exponents are equal
1. Multiply the coefficients 2. Add the exponents

29. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
3
exponent
radical sign

30. Multiplying by 10
Moving the decimal point to the right
When the exponent of a power-of-10 expression is a negative integer:
negative number
Scientific notation

31. A very small number such as 0.000000674 can be written with scientific notation as
decrease the value of the exponent by 1 (dividing by 10)
Because 4 multiplied by itself equals 16.
6.74 x 10^-7
must be multiples of 3 or 0

32. When you move the decimal point in the coefficient to the right
base
adjust the value of the coefficient
9 (3^2 = 9)
decrease the power-of-10 exponent by the same number of units

33. The decimal part
increase the power-of-10 exponent by the same number of units
coefficient
base
When moving the decimal point to the left (dividing by 10)

34. Step 1: Add the exponents Step 2: Use the common base
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left
1 divided by that number with a positive exponent
To multiply powers that have the same base:

35. 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.
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.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Engineering notation

36. 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
same exponent
1. Multiply the coefficients 2. Add the exponents
exponent

37. 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
perfect square
Moving the decimal point to the left
10^-1

38. 5^1 =
5
negative number
10^-1
1

39. Any number with a negative exponent is equal to
proper scientific
cube-root key
1 divided by that number with a positive exponent
decrease the power-of-10 exponent by the same number of units

40. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
rewrite one of the terms so that the exponents are equal
square root
change both terms in order to keep the value the same.

41. Don't bother trying to find the square root of a negative number.
1
you have to adjust the value of the exponent in order avoid changing the actual value.
The solution exists - but not in the real number system.
rewrite one of the terms so that the exponents are equal

42. 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
one digit to the left of the decimal point
increase the power-of-10 exponent by the same number of units
cube-root key

43. Valid powers of 10 for engineering notation are:
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^-2
9 (3^2 = 9)

44. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
10^2
the radical sign with a little 3 that indicates the cube root:
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

45. 1 to any power is equal to
1
rewrite one of the terms so that the exponents are equal
1. Multiply the coefficients 2. Add the exponents
10^-2

46. A number - when multiplied by itself - is equal to a given number.
10^1
square root
move the decimal point the same number of units to the left
same exponent

47. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
1. Multiply the coefficients 2. Add the exponents
0
When the exponent of a power-of-10 expression is a negative integer:

48. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
square root
1 divided by that number with a positive exponent
1

49. 1^4 =
10^1
When moving the decimal point to the left (dividing by 10)
cubed
1

50. A negative exponent does not mean the decimal value is negative. It means the decimal value is
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
a fractional decimal
negative number