Question

How do you multiply `(2a^{2} b^{3} ) ( 3a^{7} b^{5} )^{3}`?

Answer 1

`54a^23b^18`

Explanation:

`(2a^{2} b^{3} ) color(red)(( 3a^{7} b^{5} )^{3})" "larr` bracket with a power first

=`(2a^{2} b^{3} ) xxcolor(red)((27a^{21} b^{15} ))`

Now multiply the numbers and the add the indices of like bases.

=`color(blue)(2xx27) color(lime)( a^2a^21)color(magenta)( b^3 b^15)`

`color(blue)(54) color(lime)( a^23)color(magenta)( b^18)`