By what least number must 21600 be multiplied to make it a perfect cube?

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

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

N = 25/16
? ?N = ?25/16
= 5/4
= 1¹/₄

?256 / ?x = 2
? 16 = 2?x
? ?x = 8
? x = 64.

Total money donated = 4356 rupees

As total students are equal to the sum donated by each student.
Total Students =?4356
= 66

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

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

?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

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

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