How do you simplify #\root[ 3] { 8a ^ { 51} b ^ { 6} }#?

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Answer 1 · 2017-11-14T01:11:18

See a solution process below:

First, use this rule for exponents to rewrite the radical as:

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

#root(color(red)(3))(8a^51b^6) = (8a^51b^6)^(1/color(red)(3))#

Then rewrite the constant as:

#(2^3a^51b^6)^(1/color(red)(3))#

Now, use this rule of exponents to complete the simplification:

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

#(2^color(red)(3)a^color(red)(51)b^color(red)(6))^color(blue)(1/3) =>#

#2^(color(red)(3) xx color(blue)(1/3))a^(color(red)(51) xx color(blue)(1/3))b^(color(red)(6) xx color(blue)(1/3)) =>#

#2^(color(red)(3)/color(blue)(3))a^(color(red)(51)/color(blue)(3))b^(color(red)(6)/color(blue)(3)) =>#

#2^1a^17b^2 =>#

#2a^17b^2#