Question

the value of
{(23+2²)^⅔ + (150-29)^½}²​

Answer 1

$\bf \big\{ {(23 + {2}^{2} )}^{ \frac{2}{3} } + {(150 - 29)}^{ \frac{1}{2} } \big\}^{2} \\ \\ \tt\to \big\{ {(23 + 4)}^{ \frac{2}{3} } + {(121)}^{ \frac{1}{2} } \big\} ^{2} \\ \\ \to \tt \big \{ {(27)}^{ \frac{2}{3} } + \sqrt{121} \: \big\}^{2} \\ \\ \to \tt \big \{ { \big[{(27)}^{2} \big]}^{ \frac{1}{3} } + \sqrt{11 \times 11} \big\}^{2} \\ \\ \to \tt \bigg \{ \sqrt[3]{ {(27)}^{2} } + \sqrt{ {(11)}^{2} } \bigg\}^{2} \\ \\ \to \tt \bigg \{ \sqrt[3]{27 \times 27} + {( {11}^{ \cancel2} )}^{ \frac{1}{\cancel2} } \bigg\}^{2} \\ \\ \to \tt \bigg \{ \sqrt[3]{3 \times 3 \times 3 \times 3 \times 3 \times 3} + 11 \bigg\}^{2} \\ \\ \to \tt \bigg \{ \big(\sqrt[3]{3 \times 3 \times 3} \big) \times \big( \sqrt[3]{3 \times 3 \times 3} \big) + 11\bigg\}^{2} \\ \\ \to \tt \bigg \{ \bigg(\sqrt[ \cancel3]{ {(3)}^{ \cancel3} } \bigg) \times \bigg( \sqrt[ \cancel3]{ {(3)}^{ \cancel3} } \bigg) + 11 \bigg\}^{2} \\ \\ \to \tt \big \{(3 \times 3) + 11\big\}^{2} \\ \\ \to \tt \big \{ 9 + 11\big\}^{2} \: = {(20)}^{2} \: = \red{400}$

• $\rm {(a+b)}^{\frac{m}{n}} = \sqrt[n]{{(a+b)}^{m}}$