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. 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.
coefficient
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^1

2. To add powers of ten:
exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

3. Valid powers-of-10 for engineering notation
0
must be multiples of 3 or 0
1. Multiply the coefficients 2. Add the exponents
0

4. To find the square root of any number - simply key in the number (the radicand) and press the
9 (3^2 = 9)
Calculator square-root key
negative number
one digit to the left of the decimal point

5. Indicates the number of times the base is to be multiplied.
itself
0
exponent
adjust the value of the coefficient

6. 0 to any power is equal to
10^-18
coefficient
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0

7. A number with an exponent of 3 is often said to be
itself
10^2
cubed
decrease the power-of-10 exponent by the same number of units

8. 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.
cube root
1. Multiply the coefficients 2. Add the exponents
increase the power-of-10 exponent by the same number of units
Scientific notation

9. For the 10
1
2
decrease the power-of-10 exponent by the same number of units
exponent

10. Numbers with exponents can be directly multiplied or divided only when they have the
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
2
Same base

11. 1 to any power is equal to
1
1 divided by that number with a positive exponent
base
a fractional decimal

12. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1

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

14. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
Moving the decimal point to the left
1
radical sign

15. To multiply powers of 10:
decrease the value of the exponent by 1 (dividing by 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.
Engineering notation
move the decimal point the same number of units to the left

16. 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
0
cube-root key
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

17. A very small number such as 0.000000674 can be written with scientific notation as
10^-2
base
negative number
6.74 x 10^-7

18. Multiplying by 10
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the right
1
Not

19. 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
decrease the power-of-10 exponent by the same number of units
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
Calculator square-root key

20. To multiply or divide exponent terms that do not have the same base:
Subtract the exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Are Equal
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

21. Scientific notation requires there to be only
Are Equal
10^1
The solution exists - but not in the real number system.
one digit to the left of the decimal point

22. What number multiplied by itself is equal to 16? The answer is 4. Why?
negative number
Because 4 multiplied by itself equals 16.
6.74 x 10^-7
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

23. When you change the position of the decimal point in a coefficient value
0
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.
Subtract the exponent

24. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
Same base
Scientific notation
decrease the power-of-10 exponent by the same number of units

25. 100 - or 1 with the decimal point moved two places to the right
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
0
To multiply powers that have the same base:
10^2

26. Powers of ten can be added or subtracted only when their exponents
0
Are Equal
coefficient
1. Divide the coefficients 2. Subtract the exponents

27. When you move the decimal point in the coefficient to the left
square root
3
increase the power-of-10 exponent by the same number of units
a fractional decimal

28. The square root of 9 is
3
one digit to the left of the decimal point
perfect square
exponent

29. The square root of zero is
same exponent
When moving the decimal point to the left (dividing by 10)
6.74 x 10^-7
0

30. Always 10 for scientific notation
base
1. Multiply the coefficients 2. Add the exponents
The solution exists - but not in the real number system.
exponent

31. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
base
proper scientific
1. Multiply the coefficients 2. Add the exponents
1

32. 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
exponent
To multiply powers that have the same base:
1

33. The cube root of a negative number is also a
rewrite one of the terms so that the exponents are equal
1 divided by that number with a positive exponent
Same base
negative number

34. When you move the decimal point in the coefficient to the right
10^-18
radical sign
decrease the power-of-10 exponent by the same number of units
1

35. A number is a second number which - when multiplied by itself three times - equals the original number.
Moving the decimal point to the left
9 (3^2 = 9)
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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
1
you have to adjust the value of the exponent in order avoid changing the actual value.
1
change both terms in order to keep the value the same.

37. A negative exponent does not mean the decimal value is negative. It means the decimal value is
5
a fractional decimal
9 (3^2 = 9)
Calculator square-root key

38. To divide powers of 10:
Calculator square-root key
negative number
Step 1. Divide the coefficients of the terms
rewrite one of the terms so that the exponents are equal

39. When the exponents are not the same
2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
rewrite one of the terms so that the exponents are equal
cubed

40. The square of 3 is
The solution exists - but not in the real number system.
a fractional decimal
base
9 (3^2 = 9)

41. There are no special rules for adding and subtracting numbers that are written with exponents.
radical sign
adjust the value of the coefficient
9 (3^2 = 9)
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

42. 5^1 =
5
change both terms in order to keep the value the same.
a fractional decimal
exponent

43. When you increase the value of the power-of-10 exponent
proper scientific
1
2
move the decimal point the same number of units to the left

44. 1^4 =
1
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
Subtract the exponent

45. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
1 divided by that number with a positive exponent
cube-root key
Moving the decimal point to the left

46. 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
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
same exponent
2
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

47. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
Engineering notation
2
decrease the power-of-10 exponent by the same number of units
3

48. When you decrease the value of the power-of-10 exponent
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
a fractional decimal
move the decimal point the same number of units to the right

49. 3^0 =
exponent
change both terms in order to keep the value the same.
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

50. The decimal part
10^-2
2
Engineering notation
coefficient