?110¹/4 =?

Correct Answer: 101/4

Explanation:

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

Correct Answer: 0.6

Explanation:

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

Correct Answer: 10

Explanation:

21600 = 6 x 6 x 6 x 10 x 10
To, make the given number a perfect cube, it must be multiplied by 10.

Correct Answer: 450

Explanation:

3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5.

To make it a perfect cube, the given number must be divided by 2 x 3 x 3 x 5 x 5 = 450

Correct Answer: 4

Explanation:

?2401 = ?7^x
? 7^x = 2401 = 7⁴
? x = 4

Correct Answer: 324

Explanation:

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

Correct Answer: 0.3

Explanation:

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

Correct Answer: 154

Explanation:

Given that,
?16 + ?9.5 x 0.0085 x 18.9/0.021 x 0.0017 x 1.9
remove the decimal and simply the euqation.
= ?16 + ?95 x 85 x 18900/21 x 17 x 19
= 4 + ?5 x 5 x 900
= 4 + 5 x 30
= 4 + 150
= 154

Correct Answer: ?2

Explanation:

(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

Correct Answer: ?1000

Explanation:

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