(32a^(3)b^(4))/(8a^(2)b^(2))

The given expression is a simple simplification of a monomial. The rules of Indices are used in the simplification process. Basically, they involve operations on terms with the same base. We can start simplifying this equation by writing each term with same base separately.<br />Let's rewrite 32a^3b^4/8a^2b^2 as 32/8.(a^3/a^2).(b^4/b^2).<br /><br />Here after simplification:<br /><br />- For numbers, 32/8 equals 4.<br />- For terms with base 'a', the rule is subtract the exponent of 'a' in the denominator from the one in the numerator (a^3/a^2 becomes a^(3-2), hence a^1, or just 'a'). <br />- Do the same for terms with base 'b', (b^4/b^2 becomes b^(4-2), hence b^2).<br /><br />Putting it all together gives us 4*(a^1)*(b^2), which can be written simply as 4ab^2.