Simplify (x×a)^30 / (a×x)^15: Exponential Fraction Problem

The given expression is: $\frac{\left(x\times a\right)^{30}}{\left(a\times x\right)^{15}}$

To solve this, we can apply the quotient rule for exponents. The quotient rule states that $\frac{b^m}{b^n} = b^{m-n}$, where $b$ is the base and $m$ and $n$ are the exponents.

In this problem, both the numerator and the denominator have the same base $\left(x \times a\right)$. Thus, the expression simplifies by subtracting the exponents:

• The exponent of the numerator is 30.
• The exponent of the denominator is 15.

Applying the power of a quotient rule, we have:

$\left(x \times a\right)^{30-15}$

Thus, the simplified expression is $\left(x \times a\right)^{15}$.

The solution to the question is: $\left(x \times a\right)^{15}$.