Question 187173
First, simplify {{{(6a^3b)(8a^4b^2) }}}



{{{(6a^3b)(8a^4b^2) }}} Start with the given expression.



{{{(6*8)(a^3*a^4)(b*b^2) }}} Rearrange the terms.



{{{48(a^3*a^4)(b*b^2) }}} Multiply 6 and 8 to get 48



{{{48(a^(3+4))(b^(1+2)) }}} Add the exponents to multiply the monomials.



{{{48a^7*b^3}}} Add



So {{{(6a^3b)(8a^4b^2)=48a^7*b^3}}}



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This means that 



{{{((6a^3b)(8a^4b^2))/(30a^3b^2) }}} 



simplifies to 



{{{(48a^7*b^3)/(30a^3b^2) }}} 



{{{(2*2*2*2*3*a*a*a*a*a*a*a*b*b*b)/(2*3*5*a*a*a*b*b)}}} Expand. 



Note: {{{48a^7b^3=2*2*2*2*3*a*a*a*a*a*a*a*b*b*b}}} (there are 7 a's and 3 b's) and {{{30a^3b^2=2*3*5*a*a*a*b*b}}} (there are 3 a's and 3 b's)



{{{(highlight(2)*2*2*2*highlight(3)*highlight(a)*highlight(a)*highlight(a)*a*a*a*a*highlight(b)*highlight(b)*b)/(highlight(2)*highlight(3)*5*highlight(a)*highlight(a)*highlight(a)*highlight(b)*highlight(b))}}} Highlight the common terms.



{{{(cross(2)*2*2*2*cross(3)*cross(a)*cross(a)*cross(a)*a*a*a*a*cross(b)*cross(b)*b)/(cross(2)*cross(3)*5*cross(a)*cross(a)*cross(a)*cross(b)*cross(b))}}} Cancel out the common terms.



{{{(2*2*2*a*a*a*a*b)/(5)}}} Simplify.



{{{(8a^4b)/(5)}}} Regroup and multiply.



So {{{(48a^7b^3)/(30a^3b^2)}}} simplifies to {{{(8a^4b)/(5)}}}.




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Answer:



So {{{((6a^3b)(8a^4b^2))/(30a^3b^2) }}} 



simplifies to {{{(8a^4b)/(5)}}}



In other words, {{{((6a^3b)(8a^4b^2))/(30a^3b^2)=(8a^4b)/(5)}}}