Solve (12×2)⁵ Divided by (2×12)^(3y): Exponential Equation Challenge

To solve the given expression $\frac{\left(12\times2\right)^5}{\left(2\times12\right)^{3y}}$, we need to apply the rule for the power of a quotient for exponents: $\frac{a^m}{a^n} = a^{m-n}$.

The expressions in both the numerator and the denominator have the same base $\left(12 \times 2\right)$. Therefore, the expression can be rewritten as:

• Base: $\left(12 \times 2\right)$
• Exponent in the numerator: $5$
• Exponent in the denominator: $3y$

Now, applying the quotient rule:

$\frac{\left(12\times2\right)^5}{\left(2\times12\right)^{3y}} = \left(12\times2\right)^{5-3y}$

The solution to the question is:

$\left(12\times2\right)^{5-3y}$