Question

( 4^5 . 10 . 5^6 + 25^5 . 2^8 ) : ( 2^8 . 5^4 + 5^7 . 2^5 ) 

Answer 1

\(=\dfrac{2^{10}\cdot2\cdot5\cdot5^6+5^{10}\cdot2^8}{2^8\cdot5^4+5^7\cdot2^5}\)

\(=\dfrac{2^8\cdot5^7\left(2^3+5^3\right)}{2^5\cdot5^4\left(2^3+5^3\right)}=2^3\cdot5^3=10^3=1000\)

Answer 2

\(\left(4^5.10.5^6+25^5.2^8\right):\left(2^8.5^4+5^7.2^5\right)\)

\(=\dfrac{\left(2^2\right)^5.5.2.5^6+\left(5^2\right)^5.2^8}{2^8.5^4+5^7.2^5}\)

\(=\dfrac{2^{11}.5^7+5^{10}.2^8}{2^8.5^4+5^7.2^5}\)

\(=\dfrac{2^8.5^7\left(2^3+5^3\right)}{2^5.5^4\left(2^3+5^3\right)}\)

\(=2^3.5^3=\left(2.5\right)^3\)

\(=10^3=1000\)