How do you solve #(3^ { 3} ) ^ { 2} = n ^ { 6}#?

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Answer 1 · 2017-08-09T13:38:49

See a solution process below:

Use this rule of exponents to rewrite the term on the left side of the equation:

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

#(3^color(red)(3))^color(blue)(2) = n^6#

#3^(color(red)(3) xx color(blue)(2)) = n^6#

#3^6 = n^6#

Take the sixth root of each side of the equation to solve for #n# while keeping the equation balanced:

#root(6)(3^6) = root(6)(n^6)#

#3 = n#

#n = 3#