How do you write #root5((7x)^4)# as an equivalent expression using a fractional exponent?

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Answer 1 · 2017-01-10T17:17:59

#(7x)^(4/5)#

First, we need to convert this radical form to an exponent form using this rule:

#root(color(red)(n))(color(blue)(x)) = color(blue)(x)^(1/color(red)(n))#

Using this rule:

#root(color(red)(5))(color(blue)((7x)^4)) -> (color(blue)((7x)^4))^color(red)(1/5)#

We can now use this following rule for exponents to further simplify:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a)xxcolor(blue)(b))#

#(color(blue)((7x)^4))^color(red)(1/5) -> color(blue)((7x))^(4xxcolor(red)(1/5)) -> (7x)^(4/5)#