CATAlgebra > Hardx7x23\frac{x^{7}}{x^{2 \sqrt{3}}}x23x7x72x43\frac{x^{\frac{7}{2}}}{x^{\frac{4}{\sqrt{3}}}}x34x27x72x23\frac{x^{\frac{7}{2}}}{x^{2\sqrt{3}}}x23x27x7x43\frac{x^{7}}{x^{4 \sqrt{3}}}x43x7✅ Correct Option: 3Related questions:CAT 2020 Slot 1How many distinct positive integer-valued solutions exist to the equation (x2−7x+11)(x2−13x+42)=1?\left(x^{2}-7 x+11\right)^{\left(x^{2}-13 x+42\right)}=1 ?(x2−7x+11)(x2−13x+42)=1?CAT 2024 Slot 1The sum of all real values of kkk for which (18)k×(132768)13=(18)×(132768)1k\small \left( \dfrac{1}{8} \right)^k \times \left( \dfrac{1}{32768} \right)^{\frac{1}{3}} = \left( \dfrac{1}{8} \right) \times \left( \dfrac{1}{32768} \right)^{\frac{1}{k}}(81)k×(327681)31=(81)×(327681)k1 is2025 Slot 3If 1212x×424x+12×52y=84z×2012x×2433x−612^{12x}\times4^{24x+12}\times5^{2y}=8^{4z}\times20^{12x}\times243^{3x-6}1212x×424x+12×52y=84z×2012x×2433x−6, where xxx, yyy and zzz are natural numbers, then x+y+zx+y+zx+y+z equals