Limit of $\lim_{x \to 0} \frac{(1+x^5)^{10} -1}{(\sqrt{1+x^3}-1)(\sqrt[5]{1+x^2}-1) }$ I tried using symbolab to get the limit of
$$\lim_{x \to 0} \frac{(1+x^5)^{10} -1}{(\sqrt{1+x^3}-1)(\sqrt[5]{1+x^2}-1) }$$
but it couldn't solve it. With WolframAlpha I got $100$ for the limit.
Can someone show me how it's done "per hand"? I tried, but couldn't figure it out.

\begin{align*}
&\dfrac{(1+x^{5})^{10}-1}{(\sqrt{1+x^{3}}-1)(\sqrt[5]{1+x^{2}}-1)}\\
&=\dfrac{(\sqrt{1+x^{3}}+1)((1+x^{5})-1)((1+x^{5})^{9}+\cdots+1)((1+x^{2})^{4/5}+\cdots+1)}{((1+x^{3})-1)((1+x^{2})-1)}\\
&=(\sqrt{1+x^{3}}+1)((1+x^{5})^{9}+\cdots+1)((1+x^{2})^{4/5}+\cdots+1)\\
&\rightarrow 2\cdot10\cdot 5\\
&=100.
\end{align*}
