Simplify (6×3)^7 ÷ (3×6)^2: Advanced Exponent Division

Let's solve the expression step-by-step using the power of a quotient rule for exponents.

The provided expression is:

$\frac{\left(6\times3\right)^7}{\left(3\times6\right)^2}$

The power of a quotient rule states:

$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$

First, simplify the terms inside the parentheses:

• The numerator: $6 \times 3 = 18$
• The denominator: $3 \times 6 = 18$

Thus, the expression simplifies to:

$\frac{18^7}{18^2}$

We can simplify this further using the rule of dividing powers with the same base:

$\frac{a^m}{a^n} = a^{m-n}$

Apply the rule:

$\frac{18^7}{18^2} = 18^{7-2} = 18^5$

The solution to the question is: