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