Question 145303

*[Tex \LARGE sqrt{64x^{8}}] Start with the given expression



*[Tex \LARGE \left(64x^{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((64)^1x^8\right)^{\frac{1}{2}}] Rewrite 64 as {{{64^1}}}



*[Tex \LARGE (64)^{1\left(\frac{1}{2}\right)}x^{8\left(\frac{1}{2}\right)}] Now distribute the exponent Now distribute the outer exponent {{{1/2}}} to each exponent in the parenthesis. Remember {{{(x^y)^z=x^(y*z)}}}

 

*[Tex \LARGE (64)^{\frac{1}{2}}x^{\frac{8}{2}}] Now multiply the exponents

 

*[Tex \LARGE (64)^{\frac{1}{2}}x^{4}] Reduce

 

*[Tex \LARGE \sqrt{64}x^{4}] Now convert back to radical notation



*[Tex \LARGE 8x^{4}] Take the square root of 64 to get 8



So *[Tex \LARGE sqrt{64x^{8}}=8x^{4}]