Question

Pls answer. I need it urgently

Answer 1

Answer:

refer to the attachment

Answer 2

Step-by-step explanation:

To Solve:-

$\\ \:\sf{:}\longmapsto \sqrt[3]{2}\times \sqrt[4]{2}\times \sqrt[12]{32}$

Solution:-

$\\ \:\sf{:}\longmapsto \sqrt[3]{2}\times \sqrt[4]{2}\times \sqrt[12]{32}$

$\\ \:\sf{:}\longmapsto 2^{\dfrac{1}{3}}\times 2^{\dfrac{1}{4}}\times 32^{\dfrac{1}{12}}$

$\\ \:\sf{:}\longmapsto 2^{\dfrac{1}{3}}\times 2^{\dfrac{1}{4}}\times (2^{5})^{\dfrac{1}{12}}$

$\\ \:\sf{:}\longmapsto 2^{\dfrac{1}{3}}\times 2^{\dfrac{1}{4}}\times 2^{{5}\times \dfrac{1}{{12}}}$

$\\ \:\sf{:}\longmapsto 2^{\dfrac{1}{3}}\times 2^{\dfrac{1}{4}}\times 2^{\dfrac{5}{12}}$

$\\ \:\sf{:}\longmapsto 2^{\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{5}{12}}$

$\\ \:\sf{:}\longmapsto 2^{\dfrac{4+3+5}{12}}$

$\\ \:\sf{:}\longmapsto 2^{\dfrac{12}{12}}$

$\\ \:\sf{:}\longmapsto 2^1$

$\\ \:\sf{:}\longmapsto 2$

$\sf Knowledge\:Booster{\begin{cases}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{cases}}$