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)|)))