Question

plz.solve this question..... brainliest for yr and when u give details solution about both question....spams will be reported​

Answer 1

AnswEr :

☯⠀$\underline{\textsf{According to the Question Now:}}$

$:\implies\tt \large\sqrt{\sqrt[x]{2^x \sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6} \sqrt[x^4]{9^{x^{10}}}}}}}\\\\\\:\implies\tt \large\sqrt{\sqrt[x]{2^x \sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6} \times 9^{(x^{10} \times\frac{1}{x^{4}})}}}}}\\\\\\:\implies\tt \large\sqrt{\sqrt[x]{2^x \sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6} \times 9^{x^{6}}}}}}\\\\\\:\implies\tt \large\sqrt{\sqrt[x]{2^x \sqrt[x^2]{3^{x^3}\sqrt[x^3]{(6\times 9)^{x^{6}}}}}}\\\\\\:\implies\tt \large\sqrt{\sqrt[x]{2^x \sqrt[x^2]{3^{x^3}\sqrt[x^3]{54^{x^{6}}}}}}$

$\\:\implies\tt \large\sqrt{\sqrt[x]{2^x \sqrt[x^2]{3^{x^3} \times 54^{(x^{6} \times\frac{1}{x^3})}}}}\\\\\\:\implies\tt \large\sqrt{\sqrt[x]{2^x \sqrt[x^2]{3^{x^3} \times 54^{x^{3}}}}}\\\\\\:\implies\tt \large\sqrt{\sqrt[x]{2^x \sqrt[x^2]{(3\times 54)^{x^{3}}}}}\\\\\\:\implies\tt \large\sqrt{\sqrt[x]{2^x \sqrt[x^2]{162^{x^{3}}}}}\\\\\\:\implies\tt \sqrt{\sqrt[x]{2^x \times 162^{(x^{3}\times\frac{1}{x^2})}}}\\\\\\:\implies\tt \sqrt{\sqrt[x]{2^x \times 162^x}}\\\\\\:\implies\tt \sqrt{\sqrt[x]{(2 \times 162)^x}}\\\\\\:\implies\tt \sqrt{\sqrt[x]{324^x}}\\\\\\:\implies\tt \sqrt{324^{(x \:\times \:\frac{1}{x})}}\\\\\\:\implies\tt \sqrt{324}\\\\\\:\implies\tt\sqrt{18 \times 18}\\\\\\:\implies\large\underline{\boxed{\red{\tt18}}}$

⠀

$\therefore\:\underline{\textsf{Therefore, Correct Option is a) \textbf{18.}}}$

Answer 2

Given,

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}$

Here we use the identities:

• $\sqrt[n]a=a^{\frac{1}{n}}$

• $\left(a^m\right)^{\frac{1}{n}}=a^{\frac{m}{n}}$

• $\dfrac{a^m}{a^n}=a^{m-n}$

• $a^m\times b^m=(ab)^m$

Hence,

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\left(9^{x^{10}}\right)^{\frac{1}{x^4}}}}}}$

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\cdot 9^{\frac{x^{10}}{x^4}}}}}}$

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\cdot 9^{x^6}}}}}$

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{(6\times9)^{x^6}}}}}$

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\left(54^{x^6}\right)^{\frac{1}{x^3}}}}}$

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\times54^{x^3}}}}$

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{\sqrt[x]{2^x\sqrt[x^2]{(3\times54)^{x^3}}}}$

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{\sqrt[x]{2^x\left(162^{x^3}\right)^{\frac{1}{x^2}}}}$

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{\sqrt[x]{2^x\times162^x}}$

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{\sqrt[x]{(2\times162)^x}}$

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{\left(324^x\right)^{\frac{1}{x}}}$

$\longrightarrow \sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=\sqrt{324}$

$\longrightarrow\underline{\underline{\sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}}=18}}$

Hence (a) 18 is the answer.