The number of solutions of  $2^{\left|x\right|}=\sin \left(x^2\right)$

Given: $y_1=2^{\left|x\right|}, y_2=\sin \left(x^2\right).$

Comparing graphs of $y_1,y_2$, we get:

As we can see from the common graph, there is no intersection of the given curves, so there are no real solutions to $2^{\left|x\right|}=\sin x^2$.