Test your basic knowledge |

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. When you change the position of the decimal point in a coefficient value
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1 divided by that number with a positive exponent
you have to adjust the value of the exponent in order avoid changing the actual value.
proper scientific

2. 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
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 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
adjust the value of the coefficient
increase the power-of-10 exponent by the same number of units

3. 0^5 =
1. Multiply the coefficients 2. Add the exponents
0
must be multiples of 3 or 0
perfect square

4. 1 to any power is equal to
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
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
1

5. Any number with a negative exponent is equal to
0
2 x 10^9
6.74 x 10^-7
1 divided by that number with a positive exponent

6. There are no special rules for adding and subtracting numbers that are written with exponents.
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.
negative number
Are Equal

7. 1 to any power is equal to
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1
Subtract the exponent
proper scientific

8. 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
1
Not
10^-2
change both terms in order to keep the value the same.

9. Represents 1 preceded by 17 zeros and a decimal point.
Same base
2 x 10^9
10^-18
cube-root key

10. Always 10 for scientific notation
base
10^-1
must be multiples of 3 or 0
1 divided by that number with a positive exponent

11. 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.
10^1
10^-18
Scientific notation
1. Divide the coefficients 2. Subtract the exponents

12. 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
9 (3^2 = 9)
Subtract the exponent
The solution exists - but not in the real number system.

13. Increase the value of the exponent by 1 (multiplying by 10)
Not
When moving the decimal point to the left (dividing by 10)
same exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

14. To divide powers that have the same base:
itself
a fractional decimal
Not
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

15. = 0.01 - or 1 with the decimal point moved two places to the left.
2
10^-2
0
one digit to the left of the decimal point

16. The cube root of zero is
Engineering 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.
1
0

17. 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.
decrease the value of the exponent by 1 (dividing by 10)
Engineering notation
0
same exponent

18. Indicates the number of times the base is to be multiplied.
cube-root key
exponent
negative number
move the decimal point the same number of units to the left

19. To find the square root of any number - simply key in the number (the radicand) and press the
Calculator square-root key
a fractional decimal
perfect square
When moving the decimal point to the left (dividing by 10)

20. 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
6.74 x 10^-7
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
Are Equal
Step 1. Divide the coefficients of the terms

21. 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:
10^2
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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

22. When you move the decimal point in the coefficient to the left
one digit to the left of the decimal point
increase the power-of-10 exponent by the same number of units
Are Equal
adjust the value of the coefficient

23. When you increase the value of the power-of-10 exponent
1 divided by that number with a positive exponent
move the decimal point the same number of units to the left
Scientific notation
Subtract the exponent

24. A very small number such as 0.000000674 can be written with scientific notation as
When the exponent of a power-of-10 expression is a negative integer:
10^1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
6.74 x 10^-7

25. 1^4 =
0
rewrite one of the terms so that the exponents are equal
When moving the decimal point to the left (dividing by 10)
1

26. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Because 4 multiplied by itself equals 16.
squared
2 x 10^9
move the decimal point the same number of units to the left

27. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
decrease the value of the exponent by 1 (dividing by 10)
2
1
Because 4 multiplied by itself equals 16.

28. A number with an exponent of 3 is often said to be
cubed
1. Multiply the coefficients 2. Add the exponents
Because 4 multiplied by itself equals 16.
Subtract the exponent

29. Any number with an exponent of 1 is equal to
square root
cube root
itself
Subtract the exponent

30. The square root of zero is
When the exponent of a power-of-10 expression is a negative integer:
0
The solution exists - but not in the real number system.
a fractional decimal

31. Step 1: Add the exponents Step 2: Use the common base
Step 1. Divide the coefficients of the terms
increase the power-of-10 exponent by the same number of units
To multiply powers that have the same base:
must be multiples of 3 or 0

32. To multiply powers of ten:
one digit to the left of the decimal point
the radical sign with a little 3 that indicates the cube root:
1. Multiply the coefficients 2. Add the exponents
base

33. When you move the decimal point in the coefficient to the right
When the exponent of a power-of-10 expression is a negative integer:
2
decrease the power-of-10 exponent by the same number of units
increase the power-of-10 exponent by the same number of units

34. When moving the decimal point to the right (multiplying by 10)
Moving the decimal point to the left
1
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.

35. To divide powers of 10:
squared
Moving the decimal point to the left
Step 1. Divide the coefficients of the terms
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

36. The square of 3 is
9 (3^2 = 9)
squared
radical sign
increase the power-of-10 exponent by the same number of units

37. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Engineering notation
exponent
a fractional decimal
1 divided by that number with a positive exponent

38. 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.
radical sign
negative number
perfect square
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

39. Indicates the number to be multiplied.
cube root
negative number
base
exponent

40. 0 to any power is equal to
0
Engineering notation
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
decrease the value of the exponent by 1 (dividing by 10)

41. 3^0 =
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
0
square root

42. To multiply powers of 10:
change both terms in order to keep the value the same.
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.
10^1
1

43. What number multiplied by itself is equal to 16? The answer is 4. Why?
exponent
Not
Because 4 multiplied by itself equals 16.
a fractional decimal

44. 10 - or 1 with the decimal point moved one place to the right
exponent
adjust the value of the coefficient
10^1
0

45. = 0.1 - or 1 with the decimal point moved one place to the left.
Are Equal
9 (3^2 = 9)
Engineering notation
10^-1

46. Negative cube roots are okay ... negative square roots are
coefficient
move the decimal point the same number of units to the left
itself
Not

47. 100 - or 1 with the decimal point moved two places to the right
10^2
change both terms in order to keep the value the same.
decrease the value of the exponent by 1 (dividing by 10)
you have to adjust the value of the exponent in order avoid changing the actual value.

48. The decimal part
coefficient
proper scientific
Because 4 multiplied by itself equals 16.
negative number

49. The cube root of a negative number is also a
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Engineering notation
negative number
1. Multiply the coefficients 2. Add the exponents

50. When you decrease the value of the power-of-10 exponent
decrease the power-of-10 exponent by the same number of units
move the decimal point the same number of units to the right
perfect square
0