Evaluate ?16 + ?9.5 x 0.0085 x 18.9/0.021 x 0.0017 x 1.9

Given that,
⁶?0.000729
first method to solve the equation.
after removing the decimal, the equation will be
= ⁶?729/1000000
Simplify the equation.
= ⁶?3 x 3 x 3 x 3 x 3 x 3 / 10 x 10 x 10 x 10 x 10 x 10
= ⁶?3⁶/10⁶
= ⁶?( 3/10 )⁶
After simplifying the root we will get,
= ( 3/10 )^{6 x 1/6}
= 3/10
= 0.3


Second method to solve the equation.
simplify the the number in multiplication of numbers.
⁶?0.000729
⁶?0.3 x 0.3 x 0.3 x 0.3 x 0.3 x 0.3
= ⁶?(0.3)⁶
remove the root and simplify ,
= (0.3)^{6 x 1/6}
= 0.3

Given, ?x/169 = 18/13
On squaring both sides, we get
x/169 = 18/13 x 18/13
? x = 18 x 18 x 169/13 x 13
x = 18 x 18 = 324

?110¹/4
Multiply the denominator 4 with 100 and add the numerator 1.
= ?441 / 4
Simply the number in simple multiplication
= ?3 x 3 x 7 x 7 / 2 x 2
= 3 x 7/2 = 21/2
= 10.5

?105⁴/₆₄
= ?6724/64
= 82/8 = 41/4 = 10¹/₄

?0.4
= ?4/9
= 2/3 = 0.666
= 0.6

(x + 1)/(x - 1) - (x - 1)/(x + 1) = {(x + 1)² - (x - 1)²} / {(x - 1) (x + 1)}
= (x² + 1 + 2x) - (x² + 1 - 2x) / (x² - 1)
= 4x / (x² - 1) = 4(?3 + ?2) / {(?3 + ?2)² - 1}
= 4(?3 + ?2) / (3 + 2 + 2?6 - 1) = 4(?3 + ?2) / (4 + 2 ?6)
= 4(?3 + ?2) / 2 ?2 (?3 + ?2)
= ?2

?8 and ?1000 = 8^1/3 and 1000^1/3
Since 1000 > 8
? ?1000 > ?8

?81 and ?1 = 81^1/2 and 1^1/2
Since, 1 < 81
? ?1 < ?81

Let the number be x.
According to the question,
x² + (14)³ = 4425
? x² = 4425 - (14)³
? x² = 4425 - 2744
? x² = 1681
? x = ?1681 = 41

?10 and ?8 = 10^1/4 and 8^1/3
Since, LCM of 4 and 3 is 12.
? 10^1/4 = 10^3/12 = (10³)^1/12 = (1000)^1/12 = ¹²?1000
and 8^1/3 = 8^4/12 = (8⁴)^1/12 (4096)^1/2 = ¹²?4096
? 4096 > 1000
Hence, 8^1/3 >10^1/4
? ?8 > ?10