Simplify (2×3)⁶ ÷ (2×3)³: Power Division Problem

Let's solve the given expression step by step by using the power of a quotient rule for exponents. The rule states that $\frac{a^n}{a^m} = a^{n-m}$, where $a$ is any non-zero number, and $n$ and $m$ are integers.

Given the expression: $\frac{\left(2\times3\right)^{6}}{\left(2\times3\right)^3}$

• First, apply the power of a quotient rule for exponents formula: $\frac{\left(2\times3\right)^{6}}{\left(2\times3\right)^3} = \left(2\times3\right)^{6-3}$.

• The exponent in the numerator is 6, and the exponent in the denominator is 3.

• Subtract the exponent in the denominator from the exponent in the numerator: $6 - 3 = 3$.

• Thus, the expression simplifies to: $\left(2\times3\right)^3$.

The solution to the question is: $\left(2\times3\right)^{6-3}$