Question

The value of $\dfrac{6^{12}\times(35)^{28}\times(15)^{16}}{(14)^{12}\times(21)^{11}\times5^{28} }$ is ?

Answer 1

First of all :

Do prime factorisation of the bases.

Like : 6^12 = (3)^12 × (2)^12

Then,

Take the required steps .

For the full solution :

Refer to the Above Attachment !!

The required answer is =

$\frac{ {3}^{17} \times {35}^{16} }{ {4}^{11} }$

Note : Don't mind writting !! In a bit hurry !!

Answer 2

$\dfrac{6^{12}\times(35)^{28}\times(15)^{16}}{(14)^{12}\times(21)^{11}\times5^{28} }$


=
$\frac{ {(2 \times 3)}^{12} \times {(5 \times 7)}^{28} \times {(5 \times 3)}^{16} }{ {(7 \times 2)}^{12} \times {(7 \times 3)}^{11} \times {5}^{28} }$



$= \frac{ {2}^{12} \times {3}^{12} \times {5}^{28} \times { {7}^{28} \times {5}^{16} \times {3}^{16} }}{ {7}^{12} \times {2}^{12} \times {7}^{11} \times {3}^{11} \times {5}^{28} }$



$= \frac{ {2}^{12} \times {3}^{12 + 16} \times {5}^{28 + 16} \times {7}^{28} }{ {7}^{12 + 11} \times {2}^{12} \times {3}^{11} \times {5}^{28} }$



$\frac{ {2}^{12} \times {3}^{28} \times {5}^{44} \times {7}^{28} }{ {7}^{23} \times {2}^{12} \times {3}^{11} \times {5}^{28} }$



$= {2}^{12 - 12} \times {3}^{28 - 11} \times {5}^{44 - 28} \times {7}^{28 - 23}$


$= {3}^{17} \times {5}^{16} \times {7}^{5}$