Solve: Simplifying (10×4)^(6+ax) ÷ (4×10)^(4+ax) Expression

Insert the corresponding expression:

$\frac{\left(10\times4\right)^{6+ax}}{\left(4\times10\right)^{4+ax}}=$

To solve this problem, we need to simplify the given expression by applying the Power of a Quotient Rule for Exponents, which states that: $\frac{a^m}{a^n} = a^{m-n}$.

We are given the expression:

$\frac{(10 \times 4)^{6+ax}}{(4 \times 10)^{4+ax}}$

Notice that $10 \times 4$ and $4 \times 10$ are equivalent, therefore:

• $a = 10 \times 4$
• $m = 6 + ax$
• $n = 4 + ax$

Applying the quotient rule, we can write:

$\frac{a^m}{a^n} = a^{m-n}$

Inserting the values:

$a = (10 \times 4)$, $m = 6 + ax$, and $n = 4 + ax$, we obtain:

$a^{6+ax-(4+ax)}$

By simplifying the exponents:

• $(6 + ax) - (4 + ax) = 6 + ax - 4 - ax = 2$

Therefore, the expression becomes:

$(10 \times 4)^2$

The solution to the question is: $(10 \times 4)^2$