Simplify the Power Fraction: (10×3)^11 ÷ (10×3)^11

The given expression is:

$\frac{\left(10\times3\right)^{11}}{\left(10\times3\right)^{11}}$

This expression is a fraction where the numerator and the denominator are the same, both equal to $\left(10\times3\right)^{11}$.

According to the quotient rule of exponents, which states that:

• $\frac{a^m}{a^n} = a^{m-n}$, when $a$ is non-zero.

we can simplify the expression by subtracting the exponents in the denominator from the exponent in the numerator.

In our case, applying the formula:

$\frac{\left(10\times3\right)^{11}}{\left(10\times3\right)^{11}} = \left(10\times3\right)^{11-11}$

Which results in:

$\left(10\times3\right)^0$

This simplification uses the rule that any number raised to the power of zero is 1 (as long as the base is not zero). Thus, our final simplified expression $\left(10\times3\right)^0$ is indeed equal to 1.

The solution to the question is: $\left(10\times3\right)^0$.