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My Riverside Rapid Digital Portfolio

**1. Represent repeated multiplication with exponents **

You can take repeated multiplication and turn it into an exponent by counting the number of times you multiply a number by itself which becomes the base and use the number of times as the exponent.

Ex: would be because there are 4 5’s.

**2. Describe how powers represent repeated multiplication**

Powers represent repeated multiplication in the exact opposite way the number of the exponent is the amount of times you multiply the base number by itself.

Ex: would be because 6 is the exponent so there are 6 3’s.

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

The base is equal to the amount of side lengths of the model and the exponent is the amount of sides the model has.

Therefore as a model is:

and as a model is:

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

The difference in the powers and is in the first power , 2 is the base and 3 is the exponent, therefore 2 is the number you are multiplying by itself 3 times because 3 is the exponent so it would be which is equal to Whereas in the second power , 3 is the base and 2 is the exponent, therefore it would be which is equal to

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

Evaluating powers with integral basses and whole number exponents works by using repeated multiplication.

→ =

→ =

→ =

→ =

→ =

→ =

**6. Explain the role of parentheses in powers by evaluating a given set of powers such as **** , and **

When the exponent is it is which is equal to , because 4 is an equal number of negatives, this is because the – and the 2 are together in parenthesis and the exponent is outside of both of them. are the same you do BEDMAS because it is exponent first you go first which is equal to and then you multiply 16 by it’s coefficient which is -1. Therefore is equal to

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

The law for multiplying powers with the same base is keeping the base adding the exponents.

- •

With a coefficient you would multiply the coefficients by each other.

- ( ) • ( )
- and
- ( )

The law for dividing powers with the same base is subtracting the exponents.

- ÷
- or could be demonstrated with repeated multiplication
- then you would eliminate the corresponding and be left with

With coefficients you would go:

- ( ) ÷ ( )
- or could be demonstrated with repeated multiplication and then you go
- then you would eliminate the corresponding and be left with ( )

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

When raising a product or quotient to an exponent you use the power law, the rules for the power law are to keep the base multiply the exponents.

Example of power law:

→ → =

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

Any power with the exponent of 0 is equal to 1 unless the base is equal to 0.

This is because when doing BEDMAS becomes which is equal to 1. So when using the quotient law – is equal to which makes it equal to 1.

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

A pattern of powers with the same base demonstrate that when dividing the answer by the exponent you will get 1 when it comes down to zero as the exponent

=

=

=

=

=

=

=

=

=

Each time you go down you divide by the base number so in the case 2 so when it comes to zero the answer is 1.

**11. Explain the law for powers with negative exponents.**

Any base except zero raised to a negative exponent equals the reciprocal of the exponent so that it becomes positive.

ex: becomes which equals

**12. Use patterns to explain the negative exponent law**

When the exponent in the power is negative you must switch it to it’s reciprocal so that the answer can be positive. If the bases are the same the pattern will be divide every answer by 2 to get the one down.

= =

= =

= =

= =

= =

= =

= =

= =

= =

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

The exponent laws can be applied to both integral and a variable bases because the laws work on the exponent not concerning the base as long as the bases are the same.

Ex: • =

With a variable: • =

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

Error’s made in evaluating powers are either because of the product law, quotient law, power law, zero law, or negative exponents.

Here are examples of me correcting errors in expressions involving powers:

Example of power law:

Example of quotient law:

Example of product law:

Example of zero law:

Negative exponent:

**15) Use the order of operations on expressions with powers.**

Using order of operations is using BEDMAS. You use BEDMAS on expressions with powers when the bases of multiplication/division expressions aren’t the same or when you are adding and subtracting powers no matter what the base.

Example of different base mistake and correction:

Example of adding powers:

Example of subtracting powers:

**16) Determine the sum and difference of two powers.**

There is no law for finding them sum of two powers you must simply use BEDMAS so you evaluate the exponents first and then add or subtract them for your answer. Therefore to solve this equation you have to do the exponents first and then add them together.

+

+

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

Order of operations is BEDMAS, Brackets, Exponents, Division &Multiplication {in the other they happen} Addition & Subtraction {in the order they happen.} However if any of the laws apply you must do those first.

**18) Use powers to solve problems (measurement problems)**

To find the area the blue part of the square you have to go ,because 6cm is the measurement of the side lengths of the full square, minus (4) because there are 4 mini squares in white with equal side lengths of 2cm.

– (4)

= -16

= 20

To find the volume of the cube you have to go because a cube is made up of three equal sides.

= 64

To find the length of a triangle with squares you have to use the pythagorean theory which is + = . But because this figure is missing angle B not angle C you have to use subtraction and go – = .

= –

=** 36m** – **9m**

=**25m**

But 25m is the area of the square however we are looking for the side length so we have to find the square root of 25 which can either be 5 or -5 but because this is a figure it has to be greater than 0 and only 5 is therefore the answer is **5m. **

The final measurement I will demonstrate is finding the are of the blue part of the figure down below showing a circle inscribed in a square meaning it’s touching the edges of the square perfectly. The whole measurement of the figures side lengths is 13 therefore it would be minus pi multiplied by the radius of the circle squared which would be because the radius is equal to half the diameter which was 13.

= – π ( )

= 169 – π (42.25)

= 169 – 132.73

= 36.27

**19) Use powers to solve problems (growth problems)**

My pet hamsters weight triples once a month. It weighs 20 pounds now how much will it way in:

a) 2 months b)4 months c) 6 months

a) 20 x

b) 20 x

c) 20 x

Growth problems can be solved by using exponents because in this example because my hamster started at 20 pounds and is tripling every month so at 2 months it becomes 20 x 20 for the amount of pounds, 3 for the tripling and to the power of 2 because it has been 2 months of tripling which means it has to be 20 x 3 x 3. Therefore with any amount of months it would be 20 x

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

When you are applying the order of operations on expressions with powers involving negative exponents and variable bases the first thing with this question you do is the power law.

Then you would apply the quotient law by subtracting the exponents

→ →

→ →

Then you put the all the positive powers on top and the powers with the negative exponent on the bottom.

Because it is you don’t need to keep the -1 therefore you’re final answer is:

**….Anything else that you know about exponents.**

**A base raised to 1 is always equal to the base.**

Ex: =

Because with repeated multiplication is just

**1 raised to any exponent is always 1.**

Ex: =

Because =

No matter how many times you times by the answer is always .

**A coefficient is a short cut for repeated addition**

Ex: =

Example 1: exponents

Example 2: fractions

Example 3:

Example 4:

Example 5:

Example 6: Bigger size

Example 7:

Example 8:

**What is a digital footprint?**

A digital footprint is basically what it says, a permanent ‘print’ of our digital posts, anything from accomplishments to photos. This digital footprint can be found by anyone if they search up you’re name online. By ‘anyone’ it really means ANYONE; future employers, partners, universities, and even you’re kids. You’re digital footprint can affect many different opportunities weather it be positive or negative. 4 years from now when I want to get into a university/college the people who are accepting my application for admission are going to google my name. When you google my name two full pages of information come up, there are articles about my dance competitions, swimming races, public speaking festivals and information about the world partnership walk which is an organization that I raise money for every year. This to me would be something positive, when the university google’s my name they would see my accomplishments and interests. It could affect me for the better if they think that because of the positive links found under my name I would be a good applicant for the school. However what if it went the other way and the digital footprint of the person applying for a job, let say, posted offensive comments online or just not so nice language to there social media platforms. The employer would find those posts and probably not even review their application and turn them away, even if they had the perfect qualifications for the job.

What I found when i searched my name

**Strategies you can use you keep you’re digital, appropriate and safe.**

Once you’ve posted something you can never get it back, so it’s important that you keep in mind that everything you post online is accessible by anyone. If you don’t want you’re parents, teachers, siblings or friends to see what you have posted online then don’t post it because chances are they will see it. It’s also important that everything you put online is positive, because negative comments cam be taken to offense and people may take things the wrong way even if you didn’t mean to offend them personally. The saying if you don’t have anything nice to say, don’t say anything at all applies for the internet as well, if you don’t have anything

nice to post don’t post anything at all.

Someone leaving there footprints in the sand Showing how everything gets saved

**What have I learned & how will I share what I’ve learned?**

While doing this project I have learned a lot of valuable information. I didn’t know how in detail our digital footprint goes, every product we purchase and all of our information is stored somewhere and will stay there forever. It was a helpful reminder to stay safe online, and in our world where everything we do has some aspect something digital. To help spread the word about what I have learned I will bring up the subject more as it seems to be less and less talked about now a days within friend groups. People seem to ignore the truth about the internet sometimes so I will try to bring this up in places where they haven’t received this information. I will continue to keep my digital footprint and online social media accounts safe and protected to use as an example to help others.

What to read before you post Wordle with all the words connected to this post

**In conclusion I find that our digital footprint’s can be positive if we chose to live our lives in the most positive way we can. As long as we keep or posts positive, necessary, intelligent and helpful we can use the technology advancements of our time and age as an advantage to help us learn as grow as people and the world.**

Thank you,

Ashiana Sunderji

Citations:

Image 1: http://www.granvillecsd.org/webpages/lgrandjean/using_the_internet.cfm?subpage=635376

Image 2: http://qualigence.com/examining-the-resounding-effect-of-our-digital-footprint-part-2/

Image 3: https://www.pinterest.com/lastfootprint/human-footprint-humanity/

Image 4: https://www.pinterest.com/pin/466755948857948220/

Image 5: https://www.thinglink.com/scene/695259830033580034

Image 6: Made by Ashiana Sunderji using http://worldcloud.com

Short Clip: Made by Ashiana Sunderji using http://dsco.com