Simplify (x×y)^27 ÷ (x×y)^20: Exponent Division Problem

To solve the problem, we need to simplify the expression $\frac{\left(x\times y\right)^{27}}{\left(x\times y\right)^{20}}$.

We will apply the Power of a Quotient Rule for exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$.

Let's denote $a = x \times y$, and our expression becomes $\frac{a^{27}}{a^{20}}$. According to the rule:

• $m = 27$
  
• $n = 20$
  

We subtract the exponents: $m - n = 27 - 20 = 7$.

Thus, $a^{m-n} = a^7 = (x \times y)^7$.

Therefore, the expression simplifies to $\left(x \times y\right)^7$.

The solution to the question is:

$\left(x\times y\right)^7$