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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.
When the exponent of a power-of-10 expression is a negative integer:
radical sign
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
The solution exists - but not in the real number system.

2. To subtract powers of ten:
2
perfect square
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 left

3. 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
cube root
To multiply powers that have the same base:
perfect square

4. 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.
adjust the value of the coefficient
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
Same base

5. Allows you to express very large and very small numbers without using large numbers of digits and decimal places. It's all done with powers of ten.
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
radical sign
Moving the decimal point to the right

6. Any number with an exponent of 1 is equal to
To multiply powers that have the same 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
itself
Subtract the exponent

7. The square root of zero is
0
coefficient
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
one digit to the left of the decimal point

8. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
cube root
1
Step 1. Divide the coefficients of the terms

9. A negative exponent does not mean the decimal value is negative. It means the decimal value is
6.74 x 10^-7
0
When the exponent of a power-of-10 expression is a negative integer:
a fractional decimal

10. 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:
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
cube-root key
1

11. A number is a second number which - when multiplied by itself three times - equals the original number.
5
0
move the decimal point the same number of units to the left
cube root

12. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
rewrite one of the terms so that the exponents are equal
2
5
1. Divide the coefficients 2. Subtract the exponents

13. Multiplying by 10
Moving the decimal point to the right
must be multiples of 3 or 0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Step 1. Divide the coefficients of the terms

14. A number - when multiplied by itself - is equal to a given number.
a fractional decimal
square root
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Because 4 multiplied by itself equals 16.

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

16. To divide powers that have the same base:
Because 4 multiplied by itself equals 16.
itself
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
0

17. A very small number such as 0.000000674 can be written with scientific notation as
0
6.74 x 10^-7
you have to adjust the value of the exponent in order avoid changing the actual value.
exponent

18. A number with an exponent of 3 is often said to be
Step 1. Divide the coefficients of the terms
10^2
cubed
1. Multiply the coefficients 2. Add the exponents

19. 1 to any power is equal to
1
Same base
itself
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

20. 1^4 =
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1 divided by that number with a positive exponent
cube root

21. Negative cube roots are okay ... negative square roots are
The solution exists - but not in the real number system.
1
Not
1 divided by that number with a positive exponent

22. = 0.01 - or 1 with the decimal point moved two places to the left.
0
cube root
10^-2
10^1

23. Dividing by 10
you have to adjust the value of the exponent in order avoid changing the actual value.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
base
Moving the decimal point to the left

24. The cube root of a negative number is also a
negative number
adjust the value of the coefficient
1
When the exponent of a power-of-10 expression is a negative integer:

25. Indicates the number to be multiplied.
coefficient
square root
base
Are Equal

26. When you increase the value of the power-of-10 exponent
9 (3^2 = 9)
move the decimal point the same number of units to the left
1 divided by that number with a positive exponent
base

27. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
3
decrease the power-of-10 exponent by the same number of units
10^2

28. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
adjust the value of the coefficient
1
cube-root key
Subtract the exponent

29. Any number with an exponent of 0 is equal to
itself
1
change both terms in order to keep the value the same.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

30. The square of 3 is
9 (3^2 = 9)
exponent
Calculator square-root key
1

31. 10 - or 1 with the decimal point moved one place 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
10^-1
0
10^1

32. To multiply powers of 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.
0
you have to adjust the value of the exponent in order avoid changing the actual value.
Engineering notation

33. Always 10 for scientific notation
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1. Divide the coefficients 2. Subtract the exponents
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

34. 0 to any power is equal to
10^-1
same exponent
0
5

35. 5^1 =
5
When moving the decimal point to the left (dividing by 10)
2 x 10^9
increase the power-of-10 exponent by the same number of units

36. There are no special rules for adding and subtracting numbers that are written with exponents.
10^1
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
0

37. The square root of 9 is
0
0
exponent
3

38. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
1
To multiply powers that have the same base:
proper scientific

39. A number with an exponent of 2 is often said to be
squared
perfect square
9 (3^2 = 9)
0

40. When moving the decimal point to the right (multiplying by 10)
1. Multiply the coefficients 2. Add the exponents
decrease the value of the exponent by 1 (dividing by 10)
0
same exponent

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
1. Divide the coefficients 2. Subtract the exponents
exponent
change both terms in order to keep the value the same.

42. To multiply or divide exponent terms that do not have the same base:
Step 1. Evaluate each term 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
When moving the decimal point to the left (dividing by 10)
proper scientific

43. 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.
radical sign
1
1. Multiply the coefficients 2. Add the exponents
Scientific notation

44. 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
The solution exists - but not in the real number system.
itself
square root

45. When you change the position of the decimal point in a coefficient value
you have to adjust the value of the exponent in order avoid changing the actual value.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1
one digit to the left of the decimal point

46. Represents 1 preceded by 17 zeros and a decimal point.
exponent
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
10^2
10^-18

47. The symbol for the cube root of a number is
Because 4 multiplied by itself equals 16.
9 (3^2 = 9)
the radical sign with a little 3 that indicates the cube root:
The solution exists - but not in the real number system.

48. To find the square root of any number - simply key in the number (the radicand) and press the
1
Calculator square-root key
10^1
1

49. When you decrease the value of the power-of-10 exponent
0
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.
move the decimal point the same number of units to the right
To multiply powers that have the same base:

50. Numbers with exponents can be directly multiplied or divided only when they have the
1. Divide the coefficients 2. Subtract the exponents
Same base
0
2