Question

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

Answer 1

Answer:

  160

Step-by-step explanation:

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