First, use these rules of exponents to simplify the numerator:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))# and #a^color(red)(0) = 1#
#(120^color(red)(-2/5) * 120^color(blue)(2/5))/7^(-3/4) => 120^(color(red)(-2/5)+color(blue)(2/5))/7^(-3/4) =>#
#120^color(red)(0)/7^(-3/4) => 1/7^(-3/4)#
Next, we will use this rule to rewrite the expression:
#1/x^color(red)(a) = x^color(red)(-a)#
#1/7^color(red)(-3/4) = 7^color(red)(- -3/4) = 7^(3/4)#
Then, we can rewrite the expression as:
#7^(3 xx 1/4)#
Now, we can use this rule of exponents to continue the simplification:
#x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)#
#7^(color(red)(3) xx color(blue)(1/4)) => (7^color(red)(3))^color(blue)(1/4) => 343^(1/4)#
Or, using this rule: #x^(1/color(red)(n)) = root(color(red)(n))(x)#
#root(4)(343)#
