I need to show that $\qquad \displaystyle S = \{(10^p)^m \mid p \geq 0, m \geq 0\}$is not a regular language using pumping lemma.Can I multiply the product of the powers and express it to: $S = \{ 1^m 0^{pm} \mid \dots \}$ and apply the pumping lemma where I pump 1's then say that the language doesn't accept the new string? 
Pumping Lemma: is it valid to multiply the product of powers in this case?
formal languages;regular languages;pumping lemma