what operations can you assocate with coefficients? what operations can you asociate with exponents?
You can add, or multipy with each:
Example
Ax + Bx= x(A+B)
A(Bx)= AB x
x^y + x^z= x^(y+z)
[x(^y)]^z= x^yz
When working with coefficients, you can associate addition and multiplication operations.
1. Addition: When you have two terms with the same variable, say Ax and Bx, you can add them together. The sum of these terms can be obtained by adding the coefficients, that is, A + B, and multiplying it with the variable x. So, Ax + Bx can be simplified as x(A + B).
2. Multiplication: Similarly, when you have a coefficient and a term with a variable, you can multiply them together. For example, if you have A(Bx), you can simplify it by multiplying the coefficients, i.e., A times B, and keeping the variable x unchanged. Therefore, A(Bx) can be simplified as ABx.
On the other hand, when dealing with exponents, you can associate addition and multiplication operations.
1. Addition: If you have two terms with the same variable raised to different exponents, say x^y and x^z, you can add them together. The sum of these terms can be obtained by adding the exponents, that is, y + z, and keeping the base x unchanged. So, x^y + x^z can be simplified as x^(y+z).
2. Multiplication: Similarly, if you have a term with a variable raised to an exponent, and you multiply it with the same variable again raised to a different exponent, you can simplify it. For example, [x^(y)]^z can be simplified by multiplying the exponents, i.e., y times z, and keeping the base x unchanged. Thus, [x^(y)]^z simplifies to x^(yz).
Remember that these rules apply when the variables and bases are the same.