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

2.
adjust the value of the 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
10^-18
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

3. The cube root of zero is
decrease the value of the exponent by 1 (dividing by 10)
10^-1
perfect square
0

4. Multiplying by 10
perfect square
proper scientific
Moving the decimal point to the right
Same base

5. = 0.1 - or 1 with the decimal point moved one place to the left.
adjust the value of the coefficient
move the decimal point the same number of units to the right
Calculator square-root key
10^-1

6. To subtract powers of ten:
coefficient
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
3
change both terms in order to keep the value the same.

7. When you decrease the value of the power-of-10 exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
10^-2
move the decimal point the same number of units to the right
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

8. To divide powers of ten:
same exponent
2 x 10^9
1. Divide the coefficients 2. Subtract the exponents
cubed

9. Powers of ten can be added or subtracted only when their exponents
Are Equal
base
1. Divide the coefficients 2. Subtract the exponents
10^-1

10. 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.
When the exponent of a power-of-10 expression is a negative integer:
coefficient
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1

11. Always 10 for scientific notation
decrease the power-of-10 exponent by the same number of units
base
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
negative number

12. To multiply powers of 10:
9 (3^2 = 9)
10^-1
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.

13. 10 - or 1 with the decimal point moved one place to the right
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. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
radical sign
10^1

14. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
2 x 10^9
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

15. To divide powers of 10:
Moving the decimal point to the right
Step 1. Divide the coefficients of the terms
Because 4 multiplied by itself equals 16.
0

16. The cube root of a negative number is also a
Subtract the exponent
negative number
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
cube-root key

17. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
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
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Scientific notation

18. A number with an exponent of 3 is often said to be
Scientific notation
cubed
9 (3^2 = 9)
5

19. The decimal part
When moving the decimal point to the left (dividing by 10)
coefficient
exponent
2 x 10^9

20. The symbol for the cube root of a number is
perfect square
0
1
the radical sign with a little 3 that indicates the cube root:

21. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
cube-root key
Calculator square-root key
Moving the decimal point to the left

22. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
cubed
10^2
square root

23. 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
adjust the value of the coefficient
base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
a fractional decimal

24. What number multiplied by itself is equal to 16? The answer is 4. Why?
move the decimal point the same number of units to the left
adjust the value of the coefficient
Not
Because 4 multiplied by itself equals 16.

25. Valid powers-of-10 for engineering notation
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
cube root
perfect square
must be multiples of 3 or 0

26. 0^5 =
0
proper scientific
one digit to the left of the decimal point
perfect square

27. 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
a fractional decimal
2 x 10^9
Calculator square-root key

28. Dividing by 10
must be multiples of 3 or 0
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
Moving the decimal point to the left
Subtract the exponent

29. Numbers with exponents can be directly multiplied or divided only when they have the
Same base
proper scientific
0
coefficient

30. 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.
Scientific notation
radical sign
exponent
0

31. 1^4 =
1
change both terms in order to keep the value the same.
Subtract the exponent
exponent

32. 100 - or 1 with the decimal point moved two places to the right
base
cube-root key
10^2
adjust the value of the coefficient

33. To multiply powers of ten:
10^-2
negative number
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1. Multiply the coefficients 2. Add the exponents

34. When you increase the value of the power-of-10 exponent
cube root
move the decimal point the same number of units to the left
a fractional decimal
10^1

35. A number - when multiplied by itself - is equal to a given number.
Moving the decimal point to the left
square root
decrease the value of the exponent by 1 (dividing by 10)
1 divided by that number with a positive exponent

36. To multiply or divide exponent terms that do not have the same base:
Moving the decimal point to the left
1. Divide the coefficients 2. Subtract the exponents
decrease the power-of-10 exponent by the same number of units
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

37. 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
0
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
decrease the power-of-10 exponent by the same number of units
cube-root key

38. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
1. Divide the coefficients 2. Subtract the exponents
coefficient
perfect square

39. 0 to any power is equal to
0
coefficient
Not
move the decimal point the same number of units to the left

40. When moving the decimal point to the right (multiplying by 10)
1
decrease the value of the exponent by 1 (dividing by 10)
increase the power-of-10 exponent by the same number of units
Subtract the exponent

41. Indicates the number of times the base is to be multiplied.
2
exponent
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

42. Step 1: Add the exponents Step 2: Use the common base
radical sign
To multiply powers that have the same base:
10^-2
1

43. When you move the decimal point in the coefficient to the right
a fractional decimal
decrease the power-of-10 exponent by the same number of units
1. Multiply the coefficients 2. Add the exponents
perfect square

44. Any number with a negative exponent is equal to
0
1 divided by that number with a positive exponent
1
Calculator square-root key

45. Any number with an exponent of 1 is equal to
To multiply powers that have the same base:
itself
perfect square
10^2

46. 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.
cube-root key
1
3

47. To add or subtract numbers written with exponents:
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
move the decimal point the same number of units to the left
The solution exists - but not in the real number system.

48. 5^1 =
The solution exists - but not in the real number system.
squared
1
5

49. 3^0 =
same exponent
6.74 x 10^-7
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1

50. To divide powers that have the same base:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1
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)