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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 or divide exponent terms that do not have the same base:
The solution exists - but not in the real number system.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
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.
When moving the decimal point to the left (dividing by 10)

2. 1 to any power is equal to
Scientific notation
1
Engineering notation
10^2

3. A number - when multiplied by itself - is equal to a given number.
When moving the decimal point to the left (dividing by 10)
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.
square root
5

4. There are no special rules for adding and subtracting numbers that are written with exponents.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
When the exponent of a power-of-10 expression is a negative integer:
itself
0

5. Dividing by 10
1 divided by that number with a positive exponent
Calculator square-root key
Moving the decimal point to the left
5

6. Don't bother trying to find the square root of a negative number.
decrease the power-of-10 exponent by the same number of units
The solution exists - but not in the real number system.
Engineering notation
you have to adjust the value of the exponent in order avoid changing the actual value.

7. A very small number such as 0.000000674 can be written with scientific notation as
exponent
change both terms in order to keep the value the same.
6.74 x 10^-7
1

8. A number is a second number which - when multiplied by itself three times - equals the original number.
Scientific notation
Step 1. Divide the coefficients of the terms
cube root
Not

9. Powers of ten can be added or subtracted only when their exponents
Are Equal
10^1
1 divided by that number with a positive exponent
the radical sign with a little 3 that indicates the cube root:

10. To divide powers that have the same base:
Engineering notation
perfect square
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

11. To add powers of ten:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
base
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
increase the power-of-10 exponent by the same number of units

12. 5^1 =
5
10^-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
the radical sign with a little 3 that indicates the cube root:

13. 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
2
one digit to the left of the decimal point
1

14. Increase the value of the exponent by 1 (multiplying by 10)
10^-18
When moving the decimal point to the left (dividing by 10)
1
0

15. The square root of zero is
0
1. Multiply the coefficients 2. Add the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.
10^1

16. When you increase the value of the power-of-10 exponent
1
rewrite one of the terms so that the exponents are equal
move the decimal point the same number of units to the left
10^-2

17. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
coefficient
cubed
2 x 10^9
Not

18. Any number with an exponent of 0 is equal to
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Not
decrease the power-of-10 exponent by the same number of units

19. Any number with an exponent of 1 is equal to
move the decimal point the same number of units 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.
itself
Scientific notation

20. When moving the decimal point to the right (multiplying by 10)
Scientific notation
10^-1
decrease the value of the exponent by 1 (dividing by 10)
Subtract the exponent

21. When you move the decimal point in the coefficient to the right
decrease the power-of-10 exponent by the same number of units
cube-root key
10^-18
10^-1

22. Multiplying by 10
radical sign
1. Divide the coefficients 2. Subtract the exponents
0
Moving the decimal point to the right

23. 0 to any power is equal to
0
cubed
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

24. To subtract powers of ten:
Moving the decimal point to the right
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
Are Equal

25. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^-1
Engineering notation
proper scientific

26. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
adjust the value of the coefficient
Calculator square-root key
base

27. The square root of 9 is
10^-1
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. Divide the coefficients 2. Subtract the exponents

28. Indicates the number to be multiplied.
2 x 10^9
base
10^-1
one digit to the left of the decimal point

29. Step 1: Add the exponents Step 2: Use the common base
1
perfect square
To multiply powers that have the same base:
base

30. A negative exponent does not mean the decimal value is negative. It means the decimal value is
10^1
a fractional decimal
coefficient
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

31. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
Scientific notation
Step 1. Divide the coefficients of the terms
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

32. To add or subtract numbers written with exponents:
proper scientific
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
0
0

33. The cube root of zero is
perfect square
base
decrease the power-of-10 exponent by the same number of units
0

34. 1 to any power is equal to
Scientific notation
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
9 (3^2 = 9)

35. Valid powers of 10 for engineering notation are:
1 divided by that number with a positive exponent
6.74 x 10^-7
exponent
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

36. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
5
exponent
2
exponent

37. Valid powers-of-10 for engineering notation
square root
must be multiples of 3 or 0
1
cube-root key

38. To divide powers of 10:
Step 1. Divide the coefficients of the terms
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the right
Moving the decimal point to the right

39. A number with an exponent of 2 is often said to be
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1
1
squared

40. For the 10
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
exponent
you have to adjust the value of the exponent in order avoid changing the actual value.
decrease the power-of-10 exponent by the same number of units

41. 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
cube-root key
10^-2
decrease the power-of-10 exponent by the same number of units
Engineering notation

42. The cube root of a negative number is also a
cube-root key
negative number
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
2 x 10^9

43. To multiply powers of ten:
1
1. Multiply the coefficients 2. Add the exponents
cubed
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. 10 - or 1 with the decimal point moved one place to the right
negative number
rewrite one of the terms so that the exponents are equal
10^1
one digit to the left of the decimal point

45. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the left
you have to adjust the value of the exponent in order avoid changing the actual value.
move the decimal point the same number of units to the right
the radical sign with a little 3 that indicates the cube root:

46. Negative cube roots are okay ... negative square roots are
Scientific notation
Not
square root
When moving the decimal point to the left (dividing by 10)

47. 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.
5
Subtract the exponent
1. Multiply the coefficients 2. Add the exponents

48. = 0.1 - or 1 with the decimal point moved one place to the left.
Not
the radical sign with a little 3 that indicates the cube root:
10^1
10^-1

49. 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
one digit to the left of the decimal point
1. Divide the coefficients 2. Subtract the exponents
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
adjust the value of the coefficient

50.
5
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
rewrite one of the terms so that the exponents are equal
1. Multiply the coefficients 2. Add the exponents