First, rewrite this expression as:
#(4 * 8 * 3)(y^-8y^7y)(u^9u^-7)v^9 =>#
#96(y^-8y^7y)(u^9u^-7)v^9#
Next, use these rules of exponents to multiply the #y# terms:
#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))# and #a^color(red)(0) = 1#
#96(y^color(red)(-8)y^color(blue)(7)y^color(purple)(1))(u^9u^-7)v^9 =>#
#96(y^(color(red)(-8)+color(blue)(7)+color(purple)(1)))(u^9u^-7)v^9 =>#
#96(y^0)(u^9u^-7)v^9 =>#
#96(1)(u^9u^-7)v^9 =>#
#96(u^9u^-7)v^9#
Now, use this rule of exponents to multiply the #u# terms:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#
#96(u^color(red)(9)u^color(blue)(-7))v^9 =>#
#96(u^(color(red)(9)+color(blue)(-7)))v^9 =>#
#96(u^2)v^9 =>#
#96u^2v^9#