Simplify (7×2)^9 ÷ (2×7)^2: Expression with Different Exponents

To solve the given expression $\frac{\left(7\times2\right)^{9}}{\left(2\times7\right)^2}$, we will apply the Power of a Quotient Rule for Exponents. This rule states that $\frac{a^m}{a^n} = a^{m-n}$.

The base of the exponents in both the numerator and the denominator is the same, $7 \times 2$ or equivalently $2 \times 7$.

1. First, note that the structure is $\frac{(7\times2)^9}{(7\times2)^2}$.

2. Using the Power of a Quotient Rule: $\frac{(7\times2)^9}{(7\times2)^2} = (7\times2)^{9-2}$$$

3. Simplify the expression in the exponent: $9 - 2 = 7$

4. Therefore, the simplified expression is \$(7\times2)^7$

The solution to the question is: $(7\times2)^{9-2}$