Simplify (4×5)⁸ ÷ (4×5)⁴: Applying Laws of Exponents

We start with the given expression:
$\frac{\left(4\times5\right)^{8}}{\left(4\times5\right)^4}$

According to the power of a quotient rule for exponents, we can simplify an expression of the form $\frac{a^m}{a^n}$ as $a^{m-n}$.
This rule states that when we divide two exponents with the same base, we subtract the exponents.

Applying this rule to our expression, we have:

• Base: $4 \times 5$
• Exponent in the numerator: $8$
• Exponent in the denominator: $4$

Thus, we subtract the exponents in the quotient:

$(4\times5)^{8-4}$

Simplifying the exponent:

$(4\times5)^{4}$

Therefore, the expression simplifies to:
$(4\times5)^{8-4}$.

The solution to the question is $\left(4\times5\right)^{8-4}$.