What is an exponent?

Official definition: A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.

An exponent has 2 parts to it; the base and copies. The base is a large number and the copy is a smaller number raised right beside the right of the number. The copies shows how many times the base is multiplies itself by. Mathematicians made the exponent to keep multiplication expressions shorter, I think. Instead of saying 4x4x4x4, you say 4 to the power of 4. When a negative sign is introduced in the question, depending if it has brackets or not, the answers can be different. I if negative symbol is outside with no brackets, the answer will always be negative. I there are brackets in the question, it depends the amount of copies there are. If the copies are an even number, the answer will be positive, if the copies is an odd number, the answer is negative.

What is the difference between evaluating and simplifying?

Evaluating an exponent means for you to find the answer to the exponent. When a question asks you to simplify, it means to write the question in more simple terms. Usually when a question asks you to simplify a exponent, there will probably be two exponents. Sometimes you might need to use the multiplication law or division law if the exponents are doing that to each other. Example: Evaluate 5 to the power of 3. To solve the question, you need to understand and break down how to solve this. The expanded from is 5x5x5 because the base is 5 and has 3 copies of itself. 5×5 is 25, 25×5 is 125. So 125 is 5 to the power of 3 evaluated. Example: If a question says to simplify 3⁴x3², the simplified version 3⁶.

Multiplication law and why it works.

The multiplication law is when two exponents are being multiplied to each other and the bases are the same and the copies are added to each other. This law is not for solving the problem, it is just for simplifying and so are the other laws. Example: 5³x5⁴= 5⁷. 3 and 4 were the copies and added together is 7 making that the new number of copies.

Division law and why it works

The division law is the opposite of the multiplication law; instead of adding the copies, you subtract them. But, only when the question asks you to divide the exponents provided. Example: 5 to the power of 5 divided by 5⁵÷5³=5². By taking the two copies (5-3) and subtracting them equals 2.

Power of a power law and why it works

The power of a power law is when there are two copies copying the same base. To simplify, you need to multiply the two copies to each other. Example: (5⁸)⁷ turns into 5⁵⁶. 8×7=56.

One more thing you learned about exponents

Before this unit, I didn’t know how to solve a fraction with an exponent, but now I know how to solve these problems. Example: 1/3² becomes 1/9. Because 1×1=1 and 3×3=9 so the solution is 1/9

# Fossil Fuels (Solution Fluency)

Why are Fossil Fuels Bad? Can Solar Panels Replace Them?

Define: Fossil Fuels are a large problem today for humans and our environment. We want to know if it can be stopped or slowed down to prevent it from taking over. Burning fossil fuels releases a large amount of air pollutants which hurt the environment.

Discover:

Some questions can be:

• How are fossil fuels made?
• Can it be replaced?
• Are solar panels a good alternative?
• Why are solar panels good?
• Why are solar panels bad?

Deliver: There are 4 types of fossil fuels: petroleum, coal, natural gas and Orimulsion. When fossil fuels are exposed to heat, a chain made from hydrocarbon atoms converts the energy made from heat into energy made from electricity or mechanical energy. Inhaling can have negative health effects on humans and animals. These health effects include premature death, acute respiratory illness, aggravated asthma, chronic bronchitis and decreased lung function. Fossil fuels are made for driving engines and giving them power. Some examples of engines that use fossil fuels are cars and jet fuels. But, despite everything I said so far, there are some advantages to fossil fuels. They are very accessible to the public and are sold at a low price. It is also easy to transport.

Solar Panels are a very good alternative to replace fossil fuels. It is renewable at no cost to supply energy infinity. Solar panels absorb the heat energy from the sun and converts it into electricity instead of having to burn fuels and it having to affect the atmosphere. This makes solar panels environment friendly.

• Renewable Energy Source. (The most important)
• Reduces electricity bills
• Multiple applications
• Low maintenance costs
• Technology development
• Cost
• Weather dependent
• Solar energy storage is expensive

There are also some disadvantages to solar panels. Land use and habitat loss is the largest problem. Some people have solar panels on the top of their house which takes up not too much space. But, in some areas, there are square kilometers of solar panels which takes up a lot of land and could be possible habitat loss for some animals. In the making of solar panels, hazardous materials are being used while being manufactured.

Debrief: We first had to think of an idea to talk about so we both researched about different things. Then we thought of the idea to talk about solar panels so now we had to think about a question revolving around it. Fossil fuels are taking over and is unhealthy for the environment, so we wanted to compare the two. First, we had to understand what fossil fuels are and what they do, same with solar panels. Then we compared the two; with their disadvantages and advantages. After that, we thought of solutions to solve this problem.

Solution: to help this problem we could try walk also you could ask a friend to carpool or take public transit to get to work, school or anywhere you need to go. Most of the worlds power is generated by coal and natural gas so you could get solar panels installed on your roof. Eletric cars are becoming a lot more popular with how far battery technology hagotten and are becoming more affordable which can prevent fossil fuels.

Fractions and Number Lines: I already had lots of previous knowledge with number lines, but I learned more and improved on this especially when using not only fractions but also decimals on number lines. Learning negative numbers was not a problem for me. To prove this, the negative fractions stay on the left side of the zero and the positives are on the right side. If a fraction is proper and positive, it is less than one. Meaning that the numerator is smaller than the denominator.

Comparing Fractions: Most of the time I can just eye ball a fraction to know if it is larger than the other, but in this class, I need to show all off my work which has helped me complete this further. A good way is to make the denominators the same and then multiply the same number to the numerator.

Adding/Subtracting Fractions: I also had a lot of previous knowledge on this, but the trick of making the denominator the same number was stuck in my head making me understand this more. Including the negative sign caused me a little bit of trouble, but I kept practicing and later became a skill of mine. Making the denominator the same is the main and most efficient way and then doing the same to the numerator.

Multiplying/Dividing Fractions: I am very experienced in multiplying numbers in general, so multiplying fractions was very easy for me to learn and understand. Before we started dividing fractions, I forgot how to answer these types of questions, but after learning about it and how multiplying is the main tool and solution to solving the problem, I understood this rule and now I feel very confident solving this types of problems. By adding the negative sign next to a number, did not cause me any confusion on how to solve the problem. When multiplying the fractions, you multiply both of the numerators to each other and the same for the denominator. When dividing, if the denominators are not the same, then you need to reciprocate. This means that on the fraction on the right, you flip the numerator and the denominator. After this step, you just multiply the new numerators and the new denominators. Example: 3/4 ÷ 5/16 turns into 3/4 ÷ 16/5.

Square roots: I was taught how to find the square root last year, but we never elaborated on this. So practicing this made me have a better understanding on how square roots work. But one thing I still have a little of trouble with is finding the square root to a decimal, but I am still practicing this skill. To find the square root of a number, you find a number and multiply it by itself to become the square root. Example: You want to find the square root of 36. Now you need to identify what number times itself will get 36. The solution is 6*6=36. So 6 is the square root. Square root means that the root of the number is a multiple of the number you want to find the square root of. Once found the root, you need to square it.

# Dubnium

1. What? Dubnium is a highly radioactive and synthetic chemical element with the symbol of “Db” and the atomic 105. It is the most stable isotope, dubnium-268, has a half-life about of 28 hours. Theoretical research establishes dubnium as a member of group 5 in the 6d series of transition metals.
2. Who? Albert Ghiroso and the Joint Institute for Nuclear Research in Dubna who was led by Georgy Flerov.
3. Where? The Joint Institute for Nuclear Research in Dubna made the discovery in their lab in a city near Moscow. Albert Ghiroso made his discovery in a lab in California with his team
4.  When? The Joint Institute for Nuclear Research made their discovery in 1968, but in 1970 Albert Ghiroso and his team redid the experiment.
5. How? Georgy Flerov and his team bombarded americium with neon and created an isotope of an element 105. Albert Ghiroso and his team bombarded californium with neon and created isotope 261
6. Why? Georgy Flerov and his team were experimenting in their laboratory in Dubra, Russia and eventually mixed americium with neon and created the isotope.

What questions did you need to research in order to research your topic?

I answered all of the who, what, why, where, when, how questions to research on my element.

What new or familiar digital tools did you try to use as you worked on this project?

I only used reliable websites I could find while researching my element.

What was the process you used to investigate the topic?

I wrote all of the questions down and worked on each question one at a time. If I found the answer to another question, I would pause what I was doing and work on the other question.

How did you verify and cite the information you found?

I looked at many reliable websites and sources and they all said the same things or something very similar to one another. If the website was from an educational source and got their information from some other site who was reliable, then I would use it.

How did the process of completing this challenge go? What could you have done better?

The process was a bit hard because some questions I really had to dig deep and find, but I eventually found the correct answer and strived for success. There were a few times where I was distracted by something but I eventually got back on track and researched my element.