Question

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

Answer 1

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

Explanation:

`(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`