First, we can use these rules for exponents to eliminate the outer exponent:
#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#((64x^6)/(25y^2))^(-1/2) => ((64^color(red)(1)x^color(red)(6))/(25^color(red)(1)y^color(red)(2)))^color(blue)(-1/2) => (64^(color(red)(1)xxcolor(blue)(-1/2))x^(color(red)(6)xxcolor(blue)(-1/2)))/(25^(color(red)(1)xxcolor(blue)(-1/2))y^(color(red)(2)xxcolor(blue)(-1/2)) =>#
#(64^(-1/2)x^-3)/(25^(-1/2)y^-1)#
We can now use these rule of exponents to eliminate the negative exponents:
#x^color(red)(a) = 1/x^color(red)(-a)# and #1/x^color(blue)(a) = x^color(red)(-a)#
#(64^color(red)(-1/2)x^color(red)(-3))/(25^color(blue)(-1/2)y^color(blue)(-1)) => (25^color(blue)(- -1/2)y^color(blue)(-
-1))/(64^color(red)(- -1/2)x^color(red)(- -3)) => (25^(1/2)y^1)/(64^(1/2)x^3)#
Use this rule of exponents to simplify the #y# term:
#a^color(red)(1) = a#
#(25^(1/2)y^color(red)(1))/(64^(1/2)x^3) => (25^(1/2)y)/(64^(1/2)x^3)#
Now, use this rule of exponents and radicals to simplify the constants:
#x^(1/color(red)(n)) = root(color(red)(n))(x)#
#(25^(1/color(red)(2))y)/(64^(1/color(red)(2))x^3) => (root(color(red)(2))(25)y)/(root(color(red)(2))(64)x^3) => (sqrt(25)y)/(sqrt(64)x^3) => (5y)/(8x^3)#
