Chapter 11.5, Problem 66PE

Using techniques from calculus, we can show that ${\left(1+x\right)}^n=1+nx+\frac{n\left(n-1\right)x^2}{2!}+\frac{n\left(n-1\right)\left(n-2\right)}{3!}{x}^3+\cdots$ , for $\left|x\right|<1$ .

This formula can be used to evaluate binomial expressions raised to noninteger exponents. For Exercises 65-66, use the first four terms of this infinite series to approximate the given expression. Round to $3$ decimal places if necessary.

$\sqrt[4]{{\left(1.3\right)}^3}$