Question

Simplify : [ 811/2 ( 641/3 + 1251/3 ) 3 ] 1/4 i wil mark as brainlist no spamming

Answer 1

QUESTION :-

Simplify the following :- $[ 81^{\frac{1}{2} } ( 64^{\frac{1}{3} } + 125^{\frac{1}{3} } )^3 ] ^\frac{1}{4}$

SOLUTION :-

$\Rightarrow [(9^2)^{\frac{1}{2}} [(4^3)^{\frac{1}{3}} + (5^3)^{\frac{1}{3}}]^3]^\frac{1}{4} \\\\\Rightarrow [\:9 * [4 + 5]^3]^\frac{1}{4} \\\\\Rightarrow [\:9^1 * 9^3]^\frac{1}{4} \\\\\Rightarrow [\:9^{1 + 3}]^\frac{1}{4} \\\\\Rightarrow [9^4]^\frac{1}{4} \\\\=\bold 9$

LAWS USED :-

$\bold {a^\frac{1}{n} = (a^n)^\frac{1}{n} = a^1}$

$\bold {a^\frac{1}{2} = \sqrt{a}}$

$\bold {a^m * a^n = a^{m + n}}$

$\bold {(a^m)^n = a^{mn}}$