Question

The value of {(23+2²)²៸³+(140 – 19)¹៸²}², is
A. 196
B. 289
C. 324
D. 400

Answer 1

Given : {(23 + 2²)⅔ + (140 – 19)½}²

= {(23 + 4)⅔ + (140 – 19)½}²

= {(27)⅔ + (121)½}²

= {(3³)⅔ + (11²)½}²

=  {3³×⅔ + 11² ×½}²

= {3² + 11}²

= {9 + 11}²

= 20²

= 400

Hence, the value of {(23 + 2²)²៸³ + (140 – 19)¹៸²}², is 400.

Option (D) 400 is correct.

Extra information :  

Here we use the law of exponents for real numbers.

Let a (> 0) be a real number and p, q  be rational numbers, then

(a^p)^q = a^pq

 HOPE THIS ANSWER WILL HELP YOU…..

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Answer 2

Answer:

$\sf{((23 + 2^{2})^{\frac{2}{3}} + (140 - 19)^{\frac{1}{2}})^{2}}$

=> $\sf{((27)^{\frac{2}{3}} + 121^{\frac{1}{2}} )}$

=> $\sf{((3^{3})^{\frac{2}{3}} + (11^{2})^{\frac{1}{2}})^{2}}$

=> $\sf{(9 + 11)^{2}}$

=> $\sf{20^{2}}$

=> 400

Answer:- (D) 400

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