Respuesta :

gmany
[tex]16=2^4\\\\32=2^5\\\\\text{Use:}\ (a^n)^m=a^{n\cdot m}\\\\16^{2p}=32^{p+3}\\\\(2^4)^{2p}=(2^5)^{p+3}\\\\2^{4\cdot2p}=2^{5\cdot(p+3)}\\\\2^{8p}=2^{5p+15}\iff8p=5p+15\ \ \ |-5p\\\\3p=15\ \ \ \ |:3\\\\p=5[/tex]

Answer with explanation:

The equation given is

[tex](16)^{2p}=(32)^{p+3}\\\\(2^4)^{2p}=(2^5)^{p+3}\\\\2^{8p}=2^{5p+15}\\\\ \text{equating power of ,2}\\\\ 8p=5p+15\\\\8p-5p=15\\\\3p=15\\\\p=\frac{15}{3}\\\\p=5\\\\ \text{Used following law of exponents}\\\\x^{ma}=(x^m)^a[/tex]