How do you multiply # (a^2sqrt8) / (sqrt16a^6)#?

1 Answer
Mar 31, 2016

Answer:

#sqrt(2)/(2a^4)#

Explanation:

#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)|)))#