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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. Don't bother trying to find the square root of a negative number.
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 solution exists - but not in the real number system.
1. Multiply the coefficients 2. Add the exponents
When the exponent of a power-of-10 expression is a negative integer:

2. 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
square root
move the decimal point the same number of units to the right
6.74 x 10^-7

3. To find the square root of any number - simply key in the number (the radicand) and press the
0
cubed
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Calculator square-root key

4. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
cube root
10^-18
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

5. A number - when multiplied by itself - is equal to a given number.
0
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.
square root

6. The square root of zero is
To multiply powers that have the same base:
0
a fractional decimal
one digit to the left of the decimal point

7. When you move the decimal point in the coefficient to the right
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
decrease the power-of-10 exponent by the same number of units
Are Equal

8. A very small number such as 0.000000674 can be written with scientific notation as
0
one digit to the left of the decimal point
cube-root key
6.74 x 10^-7

9. Step 1: Add the exponents Step 2: Use the common base
Engineering notation
Moving the decimal point 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.
To multiply powers that have the same base:

10. When working with powers of ten and scientific notation it is often necessary to adjust the position of the decimal point in the coefficient or to change the value of the exponent. When changing one of these terms - it is important that
1
When moving the decimal point to the left (dividing by 10)
decrease the value of the exponent by 1 (dividing by 10)
change both terms in order to keep the value the same.

11. Any number with an exponent of 0 is equal to
1
0
10^-18
must be multiples of 3 or 0

12. Scientific notation requires there to be only
adjust the value of the coefficient
must be multiples of 3 or 0
one digit to the left of the decimal point
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

13. 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.
10^2
6.74 x 10^-7
Engineering notation
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

14. To divide powers that have the same base:
Are Equal
coefficient
base
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

15.
move the decimal point the same number of units to the right
0
base
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

16. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
10^-18
Calculator square-root key
10^-2
2

17. 3^0 =
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Not
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

18. When you move the decimal point in the coefficient to the left
Same base
increase the power-of-10 exponent by the same number of units
0
0

19. 0 to any power is equal to
When the exponent of a power-of-10 expression is a negative integer:
0
rewrite one of the terms so that the exponents are equal
1 divided by that number with a positive exponent

20. Always 10 for scientific notation
base
move the decimal point the same number of units to the right
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
adjust the value of the coefficient

21. 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
Moving the decimal point to the left
Same base
adjust the value of the coefficient
9 (3^2 = 9)

22. When moving the decimal point to the right (multiplying by 10)
The solution exists - but not in the real number system.
0
10^-2
decrease the value of the exponent by 1 (dividing by 10)

23. When you change the position of the decimal point in a coefficient value
Step 1. Divide the coefficients of the terms
cube-root key
you have to adjust the value of the exponent in order avoid changing the actual value.
10^1

24. 10 - or 1 with the decimal point moved one place to the right
decrease the value of the exponent by 1 (dividing by 10)
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^1
increase the power-of-10 exponent by the same number of units

25. For the 10
10^1
0
exponent
Engineering notation

26. The decimal part
0
cube-root key
coefficient
rewrite one of the terms so that the exponents are equal

27. 1^4 =
Are Equal
move the decimal point the same number of units to the right
1
When moving the decimal point to the left (dividing by 10)

28. 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.
1 divided by that number with a positive exponent
10^-2
When the exponent of a power-of-10 expression is a negative integer:
cube-root key

29. Multiplying by 10
Moving the decimal point to the right
When moving the decimal point to the left (dividing by 10)
Same base
must be multiples of 3 or 0

30. The cube root of a negative number is also a
negative number
2 x 10^9
Moving the decimal point to the left
change both terms in order to keep the value the same.

31. To multiply or divide exponent terms that do not have the same base:
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
When moving the decimal point to the left (dividing by 10)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

32. Powers of ten can be added or subtracted only when their exponents
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Are Equal
Calculator square-root key
adjust the value of the coefficient

33. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Engineering notation
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the right
Subtract the exponent

34. Any number with an exponent of 1 is equal to
radical sign
When the exponent of a power-of-10 expression is a negative integer:
itself
decrease the value of the exponent by 1 (dividing by 10)

35. To add or subtract numbers written with exponents:
2
1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

36. Negative cube roots are okay ... negative square roots are
Not
10^1
0
1 divided by that number with a positive exponent

37. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
1
1 divided by that number with a positive exponent
Because 4 multiplied by itself equals 16.
2 x 10^9

38. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
3
cube-root key
10^-18

39. When you decrease the value of the power-of-10 exponent
one digit to the left of the decimal point
base
1 divided by that number with a positive exponent
move the decimal point the same number of units to the right

40. 1 to any power is equal to
1
adjust the value of the coefficient
move the decimal point the same number of units to the left
0

41. What number multiplied by itself is equal to 16? The answer is 4. Why?
10^-2
Step 1. Divide the coefficients of the terms
0
Because 4 multiplied by itself equals 16.

42. Valid powers-of-10 for engineering notation
0
must be multiples of 3 or 0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
decrease the power-of-10 exponent by the same number of units

43. When the exponents are not the same
base
Are Equal
rewrite one of the terms so that the exponents are equal
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.

44. 5^1 =
5
10^-1
1
negative number

45. A number with an exponent of 3 is often said to be
cubed
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Engineering notation
6.74 x 10^-7

46. To multiply powers of ten:
decrease the power-of-10 exponent by the same number of units
1. Multiply the coefficients 2. Add the exponents
10^-1
10^1

47. 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
0
itself
same exponent
1. Divide the coefficients 2. Subtract the exponents

48. 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
proper scientific
change both terms in order to keep the value the same.
Engineering notation

49. The square of 3 is
9 (3^2 = 9)
1. Divide the coefficients 2. Subtract the exponents
negative number
adjust the value of the coefficient

50. 100 - or 1 with the decimal point moved two places to the right
10^2
10^-2
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