georgee2016 | George's Blog

Part 1

I am a gene. Enjoying my life in a body. It’s pretty good, you just sit there and don’t do anything. There was lots of friends to talk to, I talked to over 65000 friends each day! Everyone was perfect, just like one another, well almost. There was a group, “The naughty genes club”, this club was pretty scary, every cell in there had 3 copies of chromosome 21. Pretty scary huh? We all had two of chromosome 21, but they, they had 3. We actually always had that club, it’s pretty weird how we divide into groups in our home. I just wish that one day we could all be in one group.

The cause of Down Syndrome is pretty simple, usually cells have two chromosomes 21, but when you have Down Syndrome, you have 3 of those. Having 3 copies of chromosome 21 disrupts the course of normal development.

Part 2

In order to research this project, I needed a couple of searches on Google to find out what exactly caused Down Syndrome in individuals. I found a website published by the government that explained Down Syndrome pretty well.

Although this project is very small, it explains what Down Syndrome is pretty well, I also understood what Down Syndrome was and how it was caused.

This is my assignment for exponents

Represent repeated multiplication with exponents.

This is the basics of exponents, an exponent is a number (base) multiplied by its own using a power (number of times multiplied)

Ex: $5^3 = 5x5x5$

2. Describe how powers represent repeated multiplication

Lets say $5^6$ , 5 would be the base and 6 would be the power, it would look like this; 5x5x5x5x5x5

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

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

$2^3$ would be 2x2x2=8

$3^2$ would be 3×3=9

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

Lets say $5^2 = 25$ or $1^{8327} = 1$ or $6^4= 1296$

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

$(-2^4)$ and $-2^4$ is the same thing, $-2\cdot-2\cdot-2\cdot-2= -16$

But when the base is in parentheses like $(-2)^4$ it would be $-1\cdot-2\cdot-2\cdot-2\cdot-2= 16$

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

$4^2\cdot4^3$ as you can see, we have the same base, we would not multiply the base and add the exponents together.

It would look like this $4^{2+3} = 4^5$

$4^3\div4^2$ as you can see, we have the same base, we would not divide the base and we would subtract the exponents.

It would look like this $4^{3-2} = 4^1$

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

$4^3\div2^3$ we can see here the base isn’t the same, that means we would divide the bases and keep the exponents.

It would look like this $(4\div2)^3 = 2^3 = 8$

9. Explain the law for power with an exponent of 0

Any positive base to the power of 0 would be 1

10. Use patterns to show that a power with an exponent of 0 is equal to 1

We can use the base of 5

$5^5=3125$ $5^4=625$ $5^3=125$ $5^2=25$ $5^1=5$ $5^0=1$

As you can see, each step down, the number divides by 5

11. Explain the law for powers with negative exponents

We divide the power by the base.

12. Use patterns to explain the negative exponent law

Lets say $5^{-1}$ this would be like $1\div5 = 0,2$

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

Yes, lets say $y^5\cdot y^3$ we would do $y^{5+3} = y^8$

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

Yes, lets say $5^7\cdot5^6 = 5^{7-6}$ , this would be wrong because it doesn’t correspond to the product rules, when you do multiply a power by the same base you add the exponents together and not subtract

15. Use the order of operations on expressions with powers

$(3^3)^4 = (3^3)\cdot(3^3)\cdot(3^3)\cdot(3^3)$

= $(3x3x3)\cdot(3x3x3)\cdot(3x3x3)\cdot(3x3x3)$

= $3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3$

= $3^{12}=531441$

16. Determine the sum and difference of two powers

Sum

$5^2+6^2$ $25+36$ $= 61$

Difference:

$5^2-6^2$ $25-36$ $= -11$

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

$3\cdot9\cdot(\frac{4}{5}+5)$ $27\cdot(\frac{4}{5}+5)$ $27\cdot(5\frac{4}{5})$ $= 32\frac{4}{5}$

Here I did not use the BEDMAS rule correctly

18. Use powers to solve problems (measurement problems)

There is a rainfall in Congo, the millimeters of rain quintuples every hour and it started out with 5 millimeteres. How many millimeters of rain will there be in 1 hour? 2 hours? 5 hours?

1 hour: $5^1$ =5mm