Answer: [tex]\large\boxed{\left(a^n\right)^m=a^{nm}}[/tex]
[tex]Why?\\\\a^n=\underbrace{a\cdot a\cdot a\cdot ... \cdot a}_{n}\\\\\left(a^n\right)^m=(\underbrace{a\cdot a\cdot a\cdot ... \cdot a}_{n})^m\\\\\text{use}\ (x\cdot y)^k=x^k\cdot y^k\\\\=\underbrace{a^m\cdot a^m\cdot a^m\cdot ... \cdot a^m}_{n}\\\\\text{use}\ x^k\cdot x^l=x^{k+l}\\\\=a^{\overbrace{m+m+m+...+m}^n}=a^{n\cdot m}[/tex]
[tex]Examples:\\\\\left(2^3\right)^2=2^{3\cdot2}=2^6=64\\\left(2^3\right)^2=(8)^2=64\\\\(5^3)^{10}=5^{3\cdot10}=5^{30}[/tex]
