How do you simplify # [(4x^-4 y^2)/ (5x^6 y^-3)]^-3# leaving only positive exponents?
1 Answer
Explanation:
Given,
#((4x^-4y^2)/(5x^6y^-3))^color(blue)(-3)#
According to the exponent law ,
#=(4^(color(blue)(-3))x^((-4xxcolor(blue)(-3)))y^((2xxcolor(blue)(-3))))/(5^(color(blue)(-3))x^((6xxcolor(blue)(-3)))y^((-3xxcolor(blue)(-3))))#
Simplifying,
#=(4^-3x^12y^-6)/(5^-3x^-18y^9)#
According to the exponent law ,
#=(5^3x^(12)*5x^18)/(4^3y^9y^6)#
Simplifying,
#=(125x^(12)x^18)/(64y^9y^6)#
Using the exponent law ,
#=(125x^(12+18))/(64y^(9+6))#
#=color(green)(|bar(ul(color(white)(a/a)color(black)((125x^30)/(64y^15))color(white)(a/a)|)))#