\(\frac{1}{1-x}.\frac{1}{1+x}.\frac{1}{1+x^2}.\frac{1}{1+x^4}.\frac{1}{1+x^8}.\frac{1}{1+x^{16}}\)
\(=\frac{1}{1-x^2}.\frac{1}{1+x^2}.\frac{1}{1+x^4}.\frac{1}{1+x^8}.\frac{1}{1+x^{16}}\)
\(=\frac{1}{1-x^4}.\frac{1}{1+x^4}.\frac{1}{1+x^8}.\frac{1}{1+x^{16}}\)
\(=\frac{1}{1-x^8}.\frac{1}{1+x^8}.\frac{1}{1+x^{16}}\)
\(=\frac{1}{1-x^{16}}.\frac{1}{1+x^{16}}\)
\(=\frac{1}{1-x^{32}}\)