Simplify (10×4)² ÷ (10×4)⁵: Power Division Problem

Let's solve the given expression step by step:
$\frac{\left(10\times4\right)^2}{\left(10\times4\right)^5}$

Step 1: Use the Power of a Quotient Rule for Exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$. Here, $a = 10 \times 4$, $m = 2$, and $n = 5$.

Therefore, apply the rule:

• $\frac{\left(10\times4\right)^2}{\left(10\times4\right)^5} = \left(10\times4\right)^{2-5}$
• $= \left(10\times4\right)^{-3}$

Step 2: Convert the expression with a negative exponent to a fraction:

• We use the rule $a^{-n} = \frac{1}{a^n}$.
• Hence, $\left(10\times4\right)^{-3} = \frac{1}{\left(10\times4\right)^3}$.

The solution to the question is: $\frac{1}{\left(10\times4\right)^3}$