First, use this rule of exponents to rewrite the expression as:
#a = a^color(red)(1)#
#((2^color(red)(1)a^7)/(3^color(red)(1)b^7))^-2#
Next, use this rule of exponents to eliminate the outer exponent:
#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#((2^color(red)(1)a^color(red)(7))/(3^color(red)(1)b^color(red)(7)))^color(blue)(-2) => (2^(color(red)(1) * color(blue)(-2))a^(color(red)(7) * color(blue)(-2)))/(3^(color(red)(1) * color(blue)(-2))b^(color(red)(7) * color(blue)(-2))) => (2^-2a^-14)/(3^-2b^-14)#
Then, use these rules of exponents to eliminate the negative exponents:
#x^color(red)(a) = 1/x^color(red)(-a)# and #1/x^color(red)(a) = x^color(red)(-a)#
#(2^-2a^-14)/(3^-2b^-14) => (3^(- -2)b^(- -14))/(2^(- -2)a^(- -14)) => (3^2b^14)/(2^2a^14) =>#
#(9b^14)/(4a^14)#
