First, use these rules of exponents to remove the outer exponent:
#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#(25b^6)^-1.5 = (25^color(red)(1)b^color(red)(6))^color(blue)(-1.5) = 25^(color(red)(1) xx color(blue)(-1.5))b^(color(red)(6) xx color(blue)(-1.5)) =#
#25^-1.5b^-6.5#
We can now use this rule of exponents to eliminate the negative exponents:
#25^color(red)(-1.5)b^color(red)(-6.5) = 1/(25^color(red)(- -1.5)b^color(red)(- -6.5)) = 1/(25^1.5b^6.5)#
We can change the fractions to fractions as follows:
#1/(25^1.5b^6.5) = 1/(25^(3/2)b^(13/2))#
We can rewrite this expression as:
#1/(25^(1/2 xx 3)b^6.5)#
We can rewrite this as:
#1/((25^(1/2))^3b^6.5) = 1/(5^3b^6.5) = 1/(125b^6.5)#
