Question

A^n+1•a•a^3n. 15 баллов.

Answer 1

${a}^{n} + 1 \times a \times {a}^{3n} = {a}^{n} (1 + a \times {a}^{2n} ) \\ = {a}^{n} (1 + {a}^{2n + 1} )$

Answer 2

To simplify the expression $A^{n+1} \cdot A \cdot A^{3n}$, we can combine the exponents since all bases are the same (assuming $A$ is a non-zero constant):

When you multiply powers with the same base, you add their exponents. So, $A^{n+1} \cdot A = A^{n+1+1} = A^{n+2}$.

Then, $A^{n+2} \cdot A^{3n}$ can be further simplified by adding the exponents: $A^{n+2+3n} = A^{4n+2}$.

Thus, the final simplified expression is $A^{4n+2}$, which is equivalent to $A^2 \cdot A^{4n}$.

If this is a question or an assignment, it seems to be worth 15 points. However, please note that the value of $A$ and the context of the problem are not specified, so the expression remains in a simplified form.