1. Start by simplifying all square roots. For sqrt(8), use perfect squares to simplify.
(a^2sqrt(8))/(sqrt(16)a^6)
=(a^2sqrt(4xx2))/(4a^6)
=(a^2*2sqrt(2))/(4a^6)
=(2a^2sqrt(2))/(4a^6)
2. Factor out 2 from the numerator and denominator.
=(2(a^2sqrt(2)))/(2(2a^6))
=(color(red)cancelcolor(black)2(a^2sqrt(2)))/(color(red)cancelcolor(black)2(2a^6))
=(a^2sqrt(2))/(2a^6)
3. Use the exponent quotient law, color(purple)b^color(red)m-:color(purple)b^color(blue)n=color(purple)b^(color(red)m-color(blue)n), to simplify (a^2)/(a^6). Since the power in the denominator has a larger exponent, calculate 1/a^(6-2), instead of (a^(2-6))/1, which would save you a step.
=sqrt(2)/(2a^(6-2))
=color(green)(|bar(ul(color(white)(a/a)sqrt(2)/(2a^4)color(white)(a/a)|)))
