Question

(64a^-6b^12)^5/6
simplify the expression

Answer 1

`\left(64a^(-6)b^(12)\right)^(5)/(6)\\\\64=2^6\\\\therefore:\left(2^7a^(-6)b^(12)\right)^(5)/(6)\\\\use:(a\cdot b)^n=a^n\cdot b^n\Rightarrow\left(2^6a^(-6)b^(12)\right)^(5)/(6)=\left(2^6\right)^(5)/(6)\left(a^(-6)\right)^(5)/(6)\left(b^(12)\right)^(5)/(6)=(*)`


`use:\left(a^n\right)^m=a^(n\cdot m)\\\\(*)=2^{6\cdot(5)/(6)}\cdot a^{-6\cdot(5)/(6)}\cdot b^{12\cdot(5)/(6)}=2^5\cdot a^(-5)\cdot b^(10)=(**)\\\\We\ know:a^(-n)=\left((1)/(a)\right)^n\\\\therefore:(**)=\boxed{\boxed{(32b^(10))/(a^5)}}`