<PRE><B>Question 146712</B>


*[Tex \LARGE sqrt{49x^{12}y^4z^8}] Start with the given expression



*[Tex \LARGE \left(49x^{12}y^4z^8\right)^{\frac{1}{2}}] Convert the expression from radical notation to exponent notation. Remember *[Tex \LARGE \sqrt{\textrm{A}}=\sqrt[2]{\textrm{A}}=\textrm{A}^{\frac{1}{2}}]



*[Tex \LARGE \left((49)^1x^12y^4z^8\right)^{\frac{1}{2}}] Rewrite 49 as {{{49^1}}}



*[Tex \LARGE (49)^{1\left(\frac{1}{2}\right)}x^{12\left(\frac{1}{2}\right)}y^{4\left(\frac{1}{2}\right)}z^{8\left(\frac{1}{2}\right)}] Now distribute the outer exponent {{{1/2}}} to each exponent in the parenthesis. Remember {{{(x^y)^z=x^(y*z)}}}

 

*[Tex \LARGE (49)^{\frac{1}{2}}x^{\frac{12}{2}}y^{\frac{4}{2}}z^{\frac{8}{2}}] Now multiply the exponents

 

*[Tex \LARGE (49)^{\frac{1}{2}}x^{6}y^{2}z^{4}] Reduce

 

*[Tex \LARGE \sqrt{49}x^{6}y^{2}z^{4}] Now convert back to radical notation



*[Tex \LARGE 7x^{6}y^{2}z^{4}] Take the square root of 49 to get 7

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