Applying the sum and power rules for limits

By the sum rule for limits, $\lim_{x \to a} [f(x) + g(x)] = \lim_{x \to a} f(x) + \lim_{x \to a} g(x) = 1 + 3 = 4$.

Now apply the power rule, which states $\lim_{x \to a} [h(x)]^n = \left[\lim_{x \to a} h(x)\right]^n$ for a positive integer $n$. Here $h(x) = f(x)+g(x)$ and $n=3$, so $\lim_{x \to a} r(x) = 4^3 = 64$.

The sum rule is applied first. In part a, the sum rule was used to combine the limits of f of x and g of x into a single value, four, before that result was raised to the third power using the power rule. Applying the power rule first would not make sense, since the exponent applies to the sum of the functions, not to each function separately.