Simplify (a×b)^15 Divided by (a×b)^3: Power Division Problem

Insert the corresponding expression:

$\frac{\left(a\times b\right)^{15}}{\left(a\times b\right)^3}=$

The given expression is:
$\frac{\left(a\times b\right)^{15}}{\left(a\times b\right)^3}$

We need to apply the division rule for exponents, which states that:
$\frac{x^m}{x^n} = x^{m-n}$

Using this rule, we can simplify the expression by subtracting the exponent of the denominator from the exponent of the numerator:
$\frac{\left(a\times b\right)^{15}}{\left(a\times b\right)^3} = \left(a\times b\right)^{15-3}$

Subtracting the exponents, we have:
$\left(a\times b\right)^{12}$

Therefore, the simplified expression is:
$\left(a\times b\right)^{12}$

The solution to the question is:
$\left(a\times b\right)^{12}$