Simplify (11×12)^30 ÷ (11×12)^30: Power Division Problem

Let's solve the given mathematical expression step by step using the rules of exponents.

• We start with the expression: $\frac{\left(11\times12\right)^{30}}{\left(11\times12\right)^{30}}$.

• According to the rules of exponents, specifically the quotient rule, which states that when you divide powers with the same base, you subtract their exponents: $\frac{a^m}{a^n} = a^{m-n}$.

• Applying this rule to the expression, since the base $11 \times 12$ is the same in both the numerator and the denominator, we subtract the exponents:

  • The numerator is $\left(11\times12\right)^{30}$ and the denominator is $\left(11\times12\right)^{30}$.

  • Therefore, $\frac{\left(11\times12\right)^{30}}{\left(11\times12\right)^{30}} = \left(11\times12\right)^{30-30}$.

• Simplifying further, we have:

  • $\left(11\times12\right)^{30-30} = \left(11\times12\right)^{0}$.

  • Any non-zero number raised to the power of 0 is 1. However, here the expression is left in the form of an exponent as requested.

The solution to the question is: $\left(11\times12\right)^{30-30}$