Category Archives: Math 9

Math 9

Everything I know about exponents

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1) Represent repeated multiplication with exponents

4x4x4x4x4 = 1024 4^5 = 1024

2) Describe how powers represent repeated multiplication

The large number 4 is called the base, and the small number 5 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.

3) Demonstrate the difference between the exponent and the base by building models of a given power, such as 3^2 and 2^3.

3^2 Represents SA and 2^3 Represents Volume

4) Demonstrate the difference between two given powers in which the exponent and the base are interchanged by using repeated multiplication, such as 3^2 and 2^3.

3 x 3= 9 3^2 = 9      2 x 2 x 2 = 8 2^3 = 8

5) Evaluate powers with integral bases (excluding base 0) and whole number exponents.

5 x 5 x 5 x 5 = 625 5^4 = 625   4 x 4 x 4 x 4 x 4 = 1024  4^5 = 1024

6) Explain the role of parentheses in powers by evaluating a given set of powers such as (-2)^4 , (-2^4) and  -2^4

(-2)^4 = -2 x -2 x -2 x -2 = 16   (-2^4) = (-1 x 2 x 2 x 2 x 2) = -16    -2^4 = -1 x 2 x 2 x 2 x 2 = -16

7) Explain the exponent laws for multiplying and dividing powers with the same base.

4^2 x 4^6 = 4^8 = 65536 When multiplying keep the base and add the exponents.

4^5 ÷ 4^3 = 4^2 = 16 When dividing keep the base and subtract the exponents.

8) Explain the exponent laws for raising a product and quotient to an exponent.

2 x (6^3)^2 = 2^2 x 6^6 = 4 x 46656 = 186624 When multiplying keep the base and multiply the exponents. If there is a coefficient add the exponent to the coefficient.

9) Explain the law for powers with an exponent of zero.

When a power is raised to a zero exponent, the answer is 1, except when the base is zero

10) Use patterns to show that a power with an exponent of zero is equal to one.

2^4 = 16 2^3 = 8 2^2 = 4 2^1 = 2  2^0 = 1

11) Explain the law for powers with negative exponents.

You would have to flip the number with the negative exponent. \frac {2^{-1}}{1} = \frac {1}{2^1}

12) Use patterns to explain the negative exponent law.

\frac{1}{2} \frac{1}{4} \frac{1}{8} \frac{1}{16} \frac{1}{32} If I was dividing by 2 I wanted to go lower I would do continue the pattern. So it would go 2,4,8,16,32 and so on.

13) I can apply the exponent laws to powers with both integral and variable bases.

(-2)^3 = -8| x^6

14) I can identify the error in a simplification of an expression involving powers.

4^3 x 4^4 = 4^7 People might mistake the answer to this question as 4^{12}

15) Use the order of operations on expressions with powers

8 x 3^5 = 1944 First you would do the exponent. So then the question will become 8 x 243 = 1944

16) Determine the sum and difference of two powers.

3^6 \times 3^5 = 3^{11} = 177147| 3^6 \div 3^5 = 3^1 = 3

17) Identify the error in applying the order of operations in an incorrect solution.

(10 + 50) x 5 = 260 The correct answer is 300 because you have to do the brackets before the multiplication 60 x 5 = 300

18) Use powers to solve problems (measurement problems)

Find the volume for a cube that is 2 cm in length, width and height. 2^3 = 8 cm

19) Use powers to solve problems (growth problems)

Bacteria grows very rapidly. start with 1 bacteria and the bacteria multiplies 3 times every 1 hour. how much bacteria will there be in 10 hours? 3^{10} = 59049 There will be 59049 bacteria in 10 hours.

20) Applying the order of operations on expressions with powers involving negative exponents and variable bases.

a^{-2} x {a}^{-5} = \frac{1}{a^2} \times \frac{1}{a^5} = \frac {1}{a^7}

Math 9

Math 9

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Digital Footprint Assignment.

 

1.How might your digital footprint affect your future opportunities?

Your digital footprint could affect you because if they ever search your name they could find horrible or terrible things that could stop you from getting your dream job. It will make it a lot harder to find a good job that will make you a lot of money.

Your digital footprint could also affect you in a good way because if they don’t find anything bad about you when you try to get a job you will have a higher chance to get one because they can’t find anything bad about you.

2.Describe at least three strategies that you can use to keep your digital footprint appropriate and safe.

First strategy is to never post inappropriate stuff online because that could affect you in the future or loose your job.

Second strategy is to not use your real name on video games or websites that don’t need your info. This may save you from other people trying to steal your identity when your older.

Third strategy is to always think before you post things. You can post anything without thinking. If the message is negative, it can cost your job or your future job. You could become jobless because of the things you did in the passed even though you didn’t think it was bad for you.

3.What information did you learn that you would pass on to other students? How would you go about telling them?

I would use the information about how your digital footprint can affect your future. I would go to them when they are in a good mood and sit down together and talk about how your digital footprint can affect your future and I would give them some examples. This will help them in the future so they know anything you post that is negative can cost you the job.