Question 119124
{{{sqrt(121m^8n^4)}}} Start with the given expression.


{{{((121)^1m^8n^4)^(1/2)}}} Rewrite the square root in exponent notation. Note: {{{121}}} really looks like {{{121^1}}}



{{{(121)^(1*(1/2))m^(8*(1/2))n^(4*(1/2))}}} Now distribute the outer exponent {{{1/2}}} to each exponent in the parenthesis. Remember {{{(x^y)^z=x^(y*z)}}}



{{{(121)^(1/2)m^(8/2)n^(4/2)}}} Now multiply the exponents



{{{(121)^(1/2)m^4n^2}}} Reduce




{{{sqrt(121)m^4n^2}}} Now rewrite {{{(121)^(1/2)}}} as {{{sqrt(121)}}}




{{{11m^4n^2}}} Take the square root of 121 to get 11





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Answer:


So {{{sqrt(121m^8n^4)}}} simplifies to {{{11m^4n^2}}}.


In other words, {{{sqrt(121m^8n^4)=11m^4n^2}}}.