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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. For the 10
exponent
1. Multiply the coefficients 2. Add the exponents
1. Divide the coefficients 2. Subtract the exponents
move the decimal point the same number of units to the left

2. The square root of zero is
a fractional decimal
decrease the value of the exponent by 1 (dividing by 10)
0
itself

3. Indicates the number of times the base is to be multiplied.
increase the power-of-10 exponent by the same number of units
Moving the decimal point to the right
exponent
cubed

4. Don't bother trying to find the square root of a negative number.
adjust the value of the coefficient
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.
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.

5. 1 to any power is equal to
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
you have to adjust the value of the exponent in order avoid changing the actual value.
increase the power-of-10 exponent by the same number of units

6. Represents 1 preceded by 17 zeros and a decimal point.
0
10^-18
10^-2
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

7. To multiply or divide exponent terms that do not have the same base:
To multiply powers that have the same base:
change both terms in order to keep the value the same.
10^-2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

8. To add or subtract numbers written with exponents:
perfect square
Because 4 multiplied by itself equals 16.
base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

9. The cube root of a negative number is also a
Are Equal
increase the power-of-10 exponent by the same number of units
negative number
2 x 10^9

10. Any number with an exponent of 1 is equal to
itself
1
1. Divide the coefficients 2. Subtract the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.

11. Any number with an exponent of 0 is equal to
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
2
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

12. A number with an exponent of 3 is often said to be
cubed
Same base
increase the power-of-10 exponent by the same number of units
decrease the power-of-10 exponent by the same number of units

13. 100 - or 1 with the decimal point moved two places to the right
perfect square
square root
squared
10^2

14. The symbol for the cube root of a number is
itself
the radical sign with a little 3 that indicates the cube root:
adjust the value of the coefficient
0

15. To multiply powers of ten:
proper scientific
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1. Multiply the coefficients 2. Add the exponents

16.
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
To multiply powers that have the same base:
proper scientific
a fractional decimal

17. Numbers with exponents can be directly multiplied or divided only when they have the
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Step 1. Divide the coefficients of the terms
Same base
1. Multiply the coefficients 2. Add the exponents

18. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Step 1. Divide the coefficients of the terms
proper scientific
change both terms in order to keep the value the same.
When the exponent of a power-of-10 expression is a negative integer:

19. To add powers of ten:
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:
1 divided by that number with a positive exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

20. Always 10 for scientific notation
decrease the power-of-10 exponent by the same number of units
Same base
cubed
base

21. A number with an exponent of 2 is often said to be
Scientific notation
same exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
squared

22. The square root of 9 is
Moving the decimal point to the left
3
base
1

23. The cube root of zero is
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
exponent
Are Equal
0

24. 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.
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
perfect square
Moving the decimal point to the left
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

25. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
5
base
2
6.74 x 10^-7

26. Any number with a negative exponent is equal to
Moving the decimal point to the right
1 divided by that number with a positive exponent
0
2 x 10^9

27. = 0.01 - or 1 with the decimal point moved two places to the left.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^-2

28. 10 - or 1 with the decimal point moved one place to the right
When the exponent of a power-of-10 expression is a negative integer:
Not
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
10^1

29. 1 to any power is equal to
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
2 x 10^9
1
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

30. 0 to any power is equal to
base
Calculator square-root key
0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

31. When you increase the value of the power-of-10 exponent
square root
base
exponent
move the decimal point the same number of units to the left

32. 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
9 (3^2 = 9)
change both terms in order to keep the value the same.
Because 4 multiplied by itself equals 16.
itself

33. Scientific notation requires there to be only
proper scientific
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
one digit to the left of the decimal point

34. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
radical sign
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-18

35. 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.
1
Scientific notation
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.
increase the power-of-10 exponent by the same number of units

36. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
a fractional decimal
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^-2

37. A number - when multiplied by itself - is equal to a given number.
decrease the value of the exponent by 1 (dividing by 10)
10^1
square root
1

38. 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. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
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)
5

39. Multiplying by 10
10^2
Moving the decimal point to the right
same exponent
9 (3^2 = 9)

40. What number multiplied by itself is equal to 16? The answer is 4. Why?
the radical sign with a little 3 that indicates the cube root:
1
Because 4 multiplied by itself equals 16.
9 (3^2 = 9)

41. Increase the value of the exponent by 1 (multiplying by 10)
exponent
base
adjust the value of the coefficient
When moving the decimal point to the left (dividing by 10)

42. To find the square root of any number - simply key in the number (the radicand) and press the
cube-root key
Calculator square-root key
1
increase the power-of-10 exponent by the same number of units

43. The square of 3 is
increase the power-of-10 exponent by the same number of units
1. Multiply the coefficients 2. Add the exponents
1
9 (3^2 = 9)

44. To divide 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.
Step 1. Divide the coefficients of the terms
exponent
rewrite one of the terms so that the exponents are equal

45. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Not
0
cube root

46. Dividing by 10
Moving the decimal point to the left
10^-18
3
Subtract the exponent

47. A number is a second number which - when multiplied by itself three times - equals the original number.
When moving the decimal point to the left (dividing by 10)
Moving the decimal point to the left
coefficient
cube root

48. A negative exponent does not mean the decimal value is negative. It means the decimal value is
negative number
a fractional decimal
0
1. Multiply the coefficients 2. Add the exponents

49. 0^5 =
Same base
must be multiples of 3 or 0
0
decrease the value of the exponent by 1 (dividing by 10)

50. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
Calculator square-root key
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