Question

(-2/5)² ÷[125×8²/30⁶×(-15)²

Answer 1

\(\left(\dfrac{2}{5}\right)^2:\dfrac{125.8^2}{30^6.\left(-15\right)^2}\)

= \(\left(\dfrac{2}{5}\right)^2:\dfrac{5^3.8^2}{\left(5.6\right)^6.\left(-3.5\right)^2}\)

= \(\left(\dfrac{2}{5}\right)^2:\dfrac{2^{18}}{5^5\left(3.2\right)^6.-3^2}\)

= \(\left(\dfrac{2}{5}\right)^2:\dfrac{2^{12}}{5^5.3^6.-3^2}\)

= \(\left(\dfrac{2}{5}\right)^2.\dfrac{5^5.3^6-3^2}{2^{12}}\)

= \(\dfrac{5^4.3^6-3^2}{2^{10}}\)