How do you simplify $(2 \sqrt[3]{49}) (5 \sqrt[3]{7})$ $(2\root[ 3] { 49} ) ( 5\root [ 3] { 7} )$ ?

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Answer 1 · 2017-10-15T15:08:34

70

Given, $[2 \sqrt[3]{49}] [5 \sqrt[3]{7}]$ $[2 root(3)49][5 root(3)7]$

$\Rightarrow [2 . {(49)}^{\frac{1}{3}}] [5 . 7^{\frac{1}{3}}]$ $rArr [2. (49)^(1/3)][5. 7^(1/3)]$

$\Rightarrow 2.5 . {(7^{2})}^{\frac{1}{3}} . 7^{\frac{1}{3}}$ $rArr 2. 5. (7^2)^(1/3). 7^(1/3)$

$\Rightarrow 10 . 7^{\frac{2}{3}} {.7}^{\frac{1}{3}}$ $rArr 10. 7^(2/3).7^(1/3)$ [ As ${(a^{m})}^{n} = a^{m n}]$ $(a^m)^n = a^(mn)]$

$\Rightarrow 10 . 7^{\frac{2}{3} + \frac{1}{3}}$ $rArr 10. 7^(2/3+1/3)$ [ As $a^{m} . a^{n} = a^{m + n}]$ $a^m. a^n = a^(m+n)]$

$\Rightarrow 10 . 7^{\frac{2 + 1}{3}}$ $rArr 10. 7^[(2+1)/3]$

$\Rightarrow 10 . 7^{\frac{3}{3}}$ $rArr 10. 7^(3/3)$

$\Rightarrow 10 . 7^{1}$ $rArr 10. 7^1$

$\Rightarrow 10.7$ $rArr 10. 7$ [ As $a^{1} = a$ $a^1 = a$ ]

$\Rightarrow 70$ $rArr 70$

How do you simplify (23√49)(53√7)(2\root[ 3] { 49} ) ( 5\root [ 3] { 7} )?