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Power of powers - class-X
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Simplify: $( 16x ^{16} )^{\dfrac{3}{4}}$
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A
$8 x^{12}$
💡 Explanation:
${\left( 16{x}^{16} \right)}^{\cfrac{3}{4}} = {\left( {2}^{4} {x}^{16} \right)}^{\cfrac{3}{4}}$
$\Rightarrow \; = {\left( {2}^{4} \right)}^{\cfrac{3}{4}} {\left( {x}^{16} \right)}^{\cfrac{3}{4}}$
$\Rightarrow \; = {2}^\left( {4 \times \cfrac{3}{4}} \right) {x}^\left({16 \times \cfrac{3}{4}} \right)$
$\Rightarrow \; = {2}^{3} \times {x}^{12}$
$\Rightarrow \; = 8{x}^{12}$