Question

Hey!!!! Maths genius??? so, let's test your knowledge

$\frac{ {6}^{12} \times {35}^{28} \times {15}^{16} }{ {14}^{12} \times {21}^{11} \times {5}^{28} }$
options

${2}^{6} \times {3}^{16} \times {5}^{12}$
${3}^{17} \times {5}^{16} \times {7}^{5}$
please answer with EXPLANATION !!!

All the best

Answer 1

Answer:

3¹⁷ * 5¹⁶ * 7⁵

Step-by-step explanation:

$Given:\frac{6^{12}*35^{28}*15^{16}}{14^{12}*21^{11}*5^{28}}$

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

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

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

$=>\frac{2^{12}*3^{28}*5^{44}*7^{28}}{2^{12}*7^{23}*3^{11}*5^{28}}$

$=>\frac{3^{28}*5^{44}*7^{28}}{3^{11}*5^{28}*7^{23}}$

$=>3^{28-11}*5^{44-28}*7^{28-23}$

$=>\boxed{3^{17}*5^{16}*7^{5}}$

Hope it helps!

Answer 2

step-by-step explanation in figure attached