Question

Simplify the following rational expression without using a calculator: (12².6³.5²)/(18².15).

Answer 1

160

Explanation:

`(12^2\cdot 6^3\cdot 5^2)/(18^2\cdot 15)=((2^2\cdot 3)^2\cdot (2\cdot 3)^3\cdot 5^2)/((2\cdot 3^2)^2\cdot (3\cdot 5))\\\\=((2^4)(3^2)(2^3)(3^3)(5^2))/((2^2)(3^4)(3)(5))=(2^(4+3-2))(3^(2+3-4-1))(5^(2-1))=32\cdot 5\\\\=\bf{160}`