How do you divide and simplify #\frac { 6b ( a ^ { 2} b ) ^ { 2} } { t ( 2k ) ^ { 2} } \div \frac { 3( a b ) ^ { 2} } { ( 2kt^ 2) ^ { 3} }#?

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Answer 1 · 2017-05-31T18:39:51

#color(blue)(4a^2bkt^5#

#(6b(a^2b)^2)/(t(2k)^2)-:(3(ab)^2)/(2kt^2)^3#

#:.=(6b(a^2b)^2)/(t(2k)^2) xx ((2kt^2)^3)/(3(ab)^2)#

#:.=(6b(a^4b^2))/(t(4k^2)) xx (8k^3t^6)/(3a^2b^2)#

#:.=(6a^4b^3)/(4k^2t) xx (8k^3t^6)/(3a^2b^2)#

#:.=(6a^(4-2)b^(3-2))/4 xx (8k^(3-2)t^(6-1))/3#

#:.=(cancel6^color(blue)2a^2b)/cancel4^color(blue)1 xx (cancel8^color(blue)2kt^5)/cancel3^color(blue)1#

#:.=(2a^2b)/1 xx (2kt^5)/1#

#:.=2a^2b xx 2kt^5#

#:.color(blue)(=4a^2bkt^5#