Finding the value of the powers of 2 2^2=42^5=32 2^3=82^6=64 2^4=162^7=128
So 2^6+2^5+2^4+2^4=64+32+16+16=128=2^7
Factorising and using index laws
Notice that all of the numbers in the sum are multiples of 2^4, since 2^6=2^2\times2^4,2^5=2\times2^4,2^4=1\times2^4. So \begin{align}2^6+2^5+2^4+2^4&=2^2\times2^4+2\times2^4+1\times2^4+1\times2^4\\
&=\left(2^2+2+1+1\right)\times2^4\\
&=\left(4+2+1+1\right)\times2^4\\
&=8\times2^4\\
&=2^3\times2^4\\
&=2^7\end{align}