Question

Answer 1

\(\dfrac{2^3+2^4+2^5+2^6}{15^2}\)

\(=\dfrac{2^3\cdot\left(1+2+2^2+2^3\right)}{15^2}\)

\(=\dfrac{8\cdot\left(1+2+4+8\right)}{15^2}\)

\(=\dfrac{8\cdot15}{15^2}\)

\(=\dfrac{8}{15}\)

Answer 2

\(\dfrac{2^3+2^4+2^5+2^6}{15^2}\)

\(=\dfrac{8+16+32+64}{225}\)

\(=\dfrac{120}{225}\)

\(=\dfrac{8}{15}\)