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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. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Engineering notation
Subtract the exponent
cube root
10^2

2. Powers of ten can be added or subtracted only when their exponents
1. Multiply the coefficients 2. Add the exponents
1 divided by that number with a positive exponent
Are Equal
2 x 10^9

3. What number multiplied by itself is equal to 16? The answer is 4. Why?
square root
Because 4 multiplied by itself equals 16.
Engineering notation
3

4. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
10^1
2 x 10^9
6.74 x 10^-7
Same base

5. The square root of 9 is
3
0
Calculator square-root key
cube-root key

6. 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
same exponent
move the decimal point the same number of units to the left
10^-2
2

7. 100 - or 1 with the decimal point moved two places to the right
perfect square
10^2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the right

8. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Step 1. Divide the coefficients of the terms
a fractional decimal
decrease the value of the exponent by 1 (dividing by 10)
The solution exists - but not in the real number system.

9. Any number with an exponent of 1 is equal to
itself
move the decimal point the same number of units to the left
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Calculator square-root key

10. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
the radical sign with a little 3 that indicates the cube root:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
9 (3^2 = 9)
2

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
negative number
cube-root key
Not

12. The symbol for the cube root of a number is
10^-2
base
perfect square
the radical sign with a little 3 that indicates the cube root:

13. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
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
3
0

14. Indicates the number to be multiplied.
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
1 divided by that number with a positive exponent
base

15. When moving the decimal point to the right (multiplying by 10)
increase the power-of-10 exponent by the same number of units
change both terms in order to keep the value the same.
decrease the value of the exponent by 1 (dividing by 10)
negative number

16. 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.
decrease the power-of-10 exponent by the same number of units
perfect square
0
Moving the decimal point to the right

17. 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
change both terms in order to keep the value the same.
9 (3^2 = 9)
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

18. The square root of zero is
0
1 divided by that number with a positive exponent
10^-1
3

19. When you move the decimal point in the coefficient to the right
9 (3^2 = 9)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
radical sign
decrease the power-of-10 exponent by the same number of units

20. 10 - or 1 with the decimal point moved one place to the right
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1. Multiply the coefficients 2. Add the exponents
10^1
1

21. A number with an exponent of 2 is often said to be
squared
2
decrease the value of the exponent by 1 (dividing by 10)
0

22. To multiply or divide exponent terms that do not have the same base:
decrease the power-of-10 exponent by the same number of units
rewrite one of the terms so that the exponents are equal
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
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.

23.
1
2
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
must be multiples of 3 or 0

24. 5^1 =
2 x 10^9
move the decimal point the same number of units to the right
10^-1
5

25. 0^5 =
negative number
Step 1. Evaluate each term 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
0

26. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the left
change both terms in order to keep the value the same.
6.74 x 10^-7
move the decimal point the same number of units to the right

27. To multiply powers of 10:
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.
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
you have to adjust the value of the exponent in order avoid changing the actual value.

28. Indicates the number of times the base is to be multiplied.
exponent
square root
cube root
same exponent

29. Any number with an exponent of 0 is equal to
1
proper scientific
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
cubed

30. 1^4 =
decrease the power-of-10 exponent by the same number of units
1
10^-18
10^-1

31. A number with an exponent of 3 is often said to be
negative number
you have to adjust the value of the exponent in order avoid changing the actual value.
Because 4 multiplied by itself equals 16.
cubed

32. A number is a second number which - when multiplied by itself three times - equals the original number.
1. Multiply the coefficients 2. Add the exponents
cube root
When the exponent of a power-of-10 expression is a negative integer:
change both terms in order to keep the value the same.

33. Is a special form of power-of-10 notation where the exponents for the 10s must be 0 or multiples of 3. There must be 1 - 2 - or 3 digits on the left side of the decimal point.
you have to adjust the value of the exponent in order avoid changing the actual value.
5
Engineering notation
radical sign

34. The cube root of zero is
perfect square
Calculator square-root key
Engineering notation
0

35. Negative cube roots are okay ... negative square roots are
Not
a fractional decimal
1
cube-root key

36. When you move the decimal point in the coefficient to the left
perfect square
10^-18
0
increase the power-of-10 exponent by the same number of units

37. 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
Calculator square-root key
1
change both terms in order to keep the value the same.
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

38. Scientific notation requires there to be only
itself
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.
exponent
one digit to the left of the decimal point

39. Numbers with exponents can be directly multiplied or divided only when they have the
adjust the value of the coefficient
exponent
Same base
Calculator square-root key

40. Any number with a negative exponent is equal to
exponent
1 divided by that number with a positive exponent
same exponent
1

41. 1 to any power is equal to
cube root
Calculator square-root key
1
perfect square

42. There are no special rules for adding and subtracting numbers that are written with exponents.
squared
Not
decrease the value of the exponent by 1 (dividing by 10)
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

43. When you increase the value of the power-of-10 exponent
Because 4 multiplied by itself equals 16.
move the decimal point the same number of units to the left
When moving the decimal point to the left (dividing by 10)
10^-2

44. 1 to any power is equal to
1
move the decimal point the same number of units to the right
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Because 4 multiplied by itself equals 16.

45. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Engineering notation
Not
cube root

46. Increase the value of the exponent by 1 (multiplying by 10)
When the exponent of a power-of-10 expression is a negative integer:
When moving the decimal point to the left (dividing by 10)
radical sign
6.74 x 10^-7

47. 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
must be multiples of 3 or 0
2 x 10^9
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

48. 0 to any power is equal to
Subtract the exponent
When the exponent of a power-of-10 expression is a negative integer:
0
Not

49. A very small number such as 0.000000674 can be written with scientific notation as
change both terms in order to keep the value the same.
1 divided by that number with a positive exponent
must be multiples of 3 or 0
6.74 x 10^-7

50. 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:
base
perfect square
increase the power-of-10 exponent by the same number of units