Answer:
A^m * (A^4b^2)^n * b^3 - 3 * a^(m+1) * b^(n+2)
Explanation:
It looks like you have an expression with two terms, each containing variables raised to different exponents. Let's break down each term and see if we can simplify it.
Term 1: A^(m+4)*b^(2n+3)
This term contains two factors: A raised to the power of m+4, and b raised to the power of 2n+3. To simplify this term, we can use the rule that says a^(m+n) = a^m * a^n. Applying this rule, we have:
A^(m+4)*b^(2n+3) = A^m * A^4 * b^(2n) * b^3 = A^m * (A^4 * b^2n) * b^3 = A^m * (A^4b^2)^n * b^3
So, we can simplify the first term to:
A^m * (A^4b^2)^n * b^3
Term 2: -3a^(m+1)*b^(n+2)
This term also contains two factors: a raised to the power of m+1, and b raised to the power of n+2. To simplify this term, we can factor out a common factor of a^(m+1) and b^(n+2):
-3a^(m+1)*b^(n+2) = -3 * a^(m+1) * b^(n+2)
So, we can simplify the second term to:
-3 * a^(m+1) * b^(n+2)
Putting it all together, the original expression can be simplified to:
A^m * (A^4b^2)^n * b^3 - 3 * a^(m+1) * b^(n+2)