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CLEP General Mathematics: Powers Exponents And Roots

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. 10 - or 1 with the decimal point moved one place to the right
When moving the decimal point to the left (dividing by 10)
Not
10^1
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

2. When you decrease the value of the power-of-10 exponent
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.
squared
rewrite one of the terms so that the exponents are equal

3. What number multiplied by itself is equal to 16? The answer is 4. Why?
change both terms in order to keep the value the same.
Because 4 multiplied by itself equals 16.
decrease the value of the exponent by 1 (dividing by 10)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

4. A very small number such as 0.000000674 can be written with scientific notation as
1
6.74 x 10^-7
Are Equal
one digit to the left of the decimal point

5. Numbers with exponents can be directly multiplied or divided only when they have the
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^2
Same base
To multiply powers that have the same base:

6. To divide powers of ten:
3
1. Divide the coefficients 2. Subtract the exponents
5
2 x 10^9

7. A number with an exponent of 3 is often said to be
10^2
When moving the decimal point to the left (dividing by 10)
Scientific notation
cubed

8. 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
3
move the decimal point the same number of units to the left
same exponent
1. Multiply the coefficients 2. Add the exponents

9. Negative cube roots are okay ... negative square roots are
1
Not
move the decimal point the same number of units to the right
1

10. When you move the decimal point in the coefficient to the right
decrease the power-of-10 exponent by the same number of units
5
perfect square
1. Multiply the coefficients 2. Add the exponents

11. To subtract powers of ten:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
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
rewrite one of the terms so that the exponents are equal

12. A number - when multiplied by itself - is equal to a given number.
move the decimal point the same number of units to the left
2 x 10^9
square root
0

13. To find the square root of any number - simply key in the number (the radicand) and press the
Engineering notation
coefficient
Calculator square-root key
move the decimal point the same number of units to the left

14. Valid powers-of-10 for engineering notation
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^1
6.74 x 10^-7
must be multiples of 3 or 0

15. = 0.1 - or 1 with the decimal point moved one place to the left.
one digit to the left of the decimal point
the radical sign with a little 3 that indicates the cube root:
10^-1
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

16. 0 to any power is equal to
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0
Step 1. Divide the coefficients of the terms
squared

17. To multiply or divide exponent terms that do not have the same base:
negative number
Not
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
3

18. To divide powers that have the same base:
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.
the radical sign with a little 3 that indicates the cube root:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
6.74 x 10^-7

19. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
adjust the value of the coefficient
1
decrease the power-of-10 exponent by the same number of units
2 x 10^9

20. Powers of ten can be added or subtracted only when their exponents
0
Engineering notation
Are Equal
0

21. 5^1 =
Are Equal
cube root
5
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

22. 1^4 =
1
Calculator square-root key
must be multiples of 3 or 0
cube-root key

23. 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
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. Add the coefficients 3. Assign the common power of ten
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

24. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
1
Moving the decimal point to the left
10^2

25. 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:
Are Equal
0
coefficient

26. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
10^-1
you have to adjust the value of the exponent in order avoid changing the actual value.
the radical sign with a little 3 that indicates the cube root:

27. Indicates the number to be multiplied.
10^-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
base
itself

28. Represents 1 preceded by 17 zeros and a decimal point.
proper scientific
10^-18
change both terms in order to keep the value the same.
perfect square

29. Any number with an exponent of 0 is equal to
10^-18
base
0
1

30. Don't bother trying to find the square root of a negative number.
The solution exists - but not in the real number system.
squared
Step 1. Divide the coefficients of the terms
change both terms in order to keep the value the same.

31. When you change the position of the decimal point in a coefficient value
increase the power-of-10 exponent by the same number of units
The solution exists - but not in the real number system.
you have to adjust the value of the exponent in order avoid changing the actual value.
1. Multiply the coefficients 2. Add the exponents

32.
Subtract the exponent
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
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
rewrite one of the terms so that the exponents are equal

33. For the 10
exponent
increase the power-of-10 exponent by the same number of units
square root
1

34. 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.
To multiply powers that have the same base:
radical sign
1. Multiply the coefficients 2. Add the exponents
Calculator square-root key

35. 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
10^2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
cube root

36. 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
change both terms in order to keep the value the same.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-2
decrease the value of the exponent by 1 (dividing by 10)

37. A number with an exponent of 2 is often said to be
Engineering notation
squared
negative number
Are Equal

38. Indicates the number of times the base is to be multiplied.
rewrite one of the terms so that the exponents are equal
Moving the decimal point to the left
Calculator square-root key
exponent

39. The square root of 9 is
exponent
3
Calculator square-root key
When moving the decimal point to the left (dividing by 10)

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

41. The decimal part
1. Multiply the coefficients 2. Add the exponents
coefficient
The solution exists - but not in the real number system.
same exponent

42. 1 to any power is equal to
Calculator square-root key
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0
1

43. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
2
Because 4 multiplied by itself equals 16.
rewrite one of the terms so that the exponents are equal

44. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
10^-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
decrease the value of the exponent by 1 (dividing by 10)

45. 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
Are Equal
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
adjust the value of the coefficient
1. Multiply the coefficients 2. Add the exponents

46. When the exponents are not the same
same exponent
The solution exists - but not in the real number system.
one digit to the left of the decimal point
rewrite one of the terms so that the exponents are equal

47. 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.
adjust the value of the coefficient
0
perfect square
itself

48. The cube root of a negative number is also a
When the exponent of a power-of-10 expression is a negative integer:
base
coefficient
negative number

49. 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
radical sign
5
Scientific notation

50. Any number with an exponent of 1 is equal to
the radical sign with a little 3 that indicates the cube root:
1. Divide the coefficients 2. Subtract the exponents
itself
Because 4 multiplied by itself equals 16.