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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. A number is a second number which - when multiplied by itself three times - equals the original number.
square root
cube root
2 x 10^9
adjust the value of the coefficient

2. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
decrease the power-of-10 exponent by the same number of units
6.74 x 10^-7
1. Multiply the coefficients 2. Add the exponents

3. When you move the decimal point in the coefficient to the right
same exponent
decrease the power-of-10 exponent by the same number of units
1
10^-2

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

5. When you decrease the value of the power-of-10 exponent
10^-2
move the decimal point the same number of units to the right
When moving the decimal point to the left (dividing by 10)
Are Equal

6. A very small number such as 0.000000674 can be written with scientific notation as
perfect square
6.74 x 10^-7
a fractional decimal
base

7. 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.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
square root
base
When the exponent of a power-of-10 expression is a negative integer:

8. There are no special rules for adding and subtracting numbers that are written with exponents.
square root
must be multiples of 3 or 0
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

9. The square root of zero is
Because 4 multiplied by itself equals 16.
decrease the value of the exponent by 1 (dividing by 10)
1
0

10. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
decrease the value of the exponent by 1 (dividing by 10)
The solution exists - but not in the real number system.
perfect square

11. 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.
one digit to the left of the decimal point
radical sign
you have to adjust the value of the exponent in order avoid changing the actual value.
3

12. Always 10 for scientific notation
radical sign
Scientific notation
base
rewrite one of the terms so that the exponents are equal

13. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
negative number
move the decimal point the same number of units to the right
proper scientific

14. 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.
10^-2
Not
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Scientific notation

15. 0^5 =
move the decimal point the same number of units to the right
0
negative number
adjust the value of the coefficient

16. To multiply or divide exponent terms that do not have the same base:
one digit to the left of the decimal point
itself
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

17. Scientific notation requires there to be only
one digit to the left of the decimal point
0
proper scientific
cubed

18. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
5
0
Calculator square-root key

19. The decimal part
Are Equal
coefficient
perfect square
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

20. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
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
a fractional decimal
5

21. 3^0 =
square root
base
you have to adjust the value of the exponent in order avoid changing the actual value.
1

22. Negative cube roots are okay ... negative square roots are
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1
1
Not

23. 100 - or 1 with the decimal point moved two places to the right
1. Divide the coefficients 2. Subtract the exponents
change both terms in order to keep the value the same.
you have to adjust the value of the exponent in order avoid changing the actual value.
10^2

24. Indicates the number of times the base is to be multiplied.
To multiply powers that have the same base:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
exponent
0

25. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Same base
2 x 10^9
one digit to the left of the decimal point
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.

26. To subtract powers of ten:
1. Multiply the coefficients 2. Add the exponents
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Because 4 multiplied by itself equals 16.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

27. What number multiplied by itself is equal to 16? The answer is 4. Why?
Same base
proper scientific
Because 4 multiplied by itself equals 16.
change both terms in order to keep the value the same.

28. The square root of 9 is
3
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
6.74 x 10^-7

29. Multiplying by 10
one digit to the left of the decimal point
Same base
Moving the decimal point to the right
When the exponent of a power-of-10 expression is a negative integer:

30. 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
decrease the power-of-10 exponent by the same number of units
rewrite one of the terms so that the exponents are equal
cube-root key
Calculator square-root key

31. To find the square root of any number - simply key in the number (the radicand) and press the
exponent
Calculator square-root key
proper scientific
one digit to the left of the decimal point

32. = 0.1 - or 1 with the decimal point moved one place to the left.
5
10^-1
0
When the exponent of a power-of-10 expression is a negative integer:

33. 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
decrease the value of the exponent by 1 (dividing by 10)
same exponent
Moving the decimal point to the left
0

34. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Moving the decimal point to the right
radical sign
Subtract the exponent
2 x 10^9

35. To divide powers of 10:
Step 1. Divide the coefficients of the terms
1
the radical sign with a little 3 that indicates the cube root:
1

36. The cube root of a negative number is also a
negative number
0
move the decimal point the same number of units to the right
Moving the decimal point to the left

37. Any number with an exponent of 1 is equal to
When moving the decimal point to the left (dividing by 10)
itself
Moving the decimal point to the right
squared

38. To multiply powers of 10:
The solution exists - but not in the real number system.
Step 1. Divide the coefficients of the terms
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

39. Don't bother trying to find the square root of a negative number.
one digit to the left of the decimal point
9 (3^2 = 9)
5
The solution exists - but not in the real number system.

40. 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
10^-1
negative number
3

41. Step 1: Add the exponents Step 2: Use the common base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Moving the decimal point to the right
To multiply powers that have the same base:
move the decimal point the same number of units to the right

42.
must be multiples of 3 or 0
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
decrease the value of the exponent by 1 (dividing by 10)

43. 1 to any power is equal to
1
exponent
When the exponent of a power-of-10 expression is a negative integer:
move the decimal point the same number of units to the right

44. Valid powers of 10 for engineering notation are:
10^-1
coefficient
increase the power-of-10 exponent by the same number of units
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

45. When you change the position of the decimal point in a coefficient value
When the exponent of a power-of-10 expression is a negative integer:
1. Divide the coefficients 2. Subtract the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

46. The square of 3 is
1
proper scientific
the radical sign with a little 3 that indicates the cube root:
9 (3^2 = 9)

47. To divide powers that have the same base:
2 x 10^9
2
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
same exponent

48. 5^1 =
5
1
change both terms in order to keep the value the same.
base

49. When moving the decimal point to the right (multiplying by 10)
1
Because 4 multiplied by itself equals 16.
decrease the value of the exponent by 1 (dividing by 10)
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

50. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
6.74 x 10^-7
10^1
5