Question

How do you write a general rule for finding a power of a power?​

Answer 1

Answer:
`\large\boxed{\left(a^n\right)^m=a^(nm)}`

`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)`

`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)`