First, rewrite the expression as:
#(4 * 9)(a^3 * a^-5)(b^-2 * b) =>#
#36(a^3 * a^-5)(b^-2 * b)#
Next, use this rule of exponents to rewrite #b#:
#x = x^color(blue)(1)#
#36(a^3 * a^-5)(b^-2 * b^color(blue)(1))#
Then, use this rule of exponents to multiply the #a# and #b# terms:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#
#36(a^color(red)(3) * a^color(blue)(-5))(b^color(red)(-2) * b^color(blue)(1)) =>#
#36a^(color(red)(3)+color(blue)(-5))b^(color(red)(-2)+color(blue)(1)) =>#
#36a^-2b^-1#
Next, use this rule of exponents to eliminate the negative exponents:
#x^color(red)(a) = 1/x^color(red)(-a)#
#36a^color(red)(-2)b^color(red)(-1) =>#
#36/(a^color(red)(- -2)b^color(red)(- -1)) =>#
#36/(a^2b^1)#
Now, use this rule of exponents to complete the simplification:
#x^color(red)(1) = x#
#36/(a^2b^color(red)(1)) =>#
#36/(a^2b)#
