Question

Simplify, giving solution with positive index​ : $(4x^2{y}^3{)}^3÷(3x^2{y}^3{)}^3$

Answer 1

Given : $(4x^2{y}^3{)}^3÷(3x^2{y}^3{)}^3$
It can be written as:
$(4x^2{y}^3{)}^3÷(3x^2{y}^3{)}^3=\frac{4^3{x}^{2\times 3}{y}^{3\times 3}}{3^3{x}^{2\times 3}{y}^{3\times 3}}$
[$\because$ $(a^m{)}^n=a^{mn}$]

On further calculation , we have :
$(4x^2{y}^3{)}^3÷(3x^2{y}^3{)}^3=\frac{4^3{x}^6{y}^9}{3^3{x}^6{y}^9}$

$=\frac{4^3{x}^{6-6}{y}^{9-9}}{3^3}$

$=\frac{4^3{x}^0{y}^0}{3^3}=\frac{4^3}{3^3}$
$=\frac{64}{27}$ [$\because$ $a^0=1$]

Hence, $(4x^2{y}^3{)}^3÷(3x^2{y}^3{)}^3=\frac{64}{27}$