How do you divide #(2a ^ { 2} b ^ { 3} ) ^ { 4} \div 4a ^ { 5} b ^ { 2}#?

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Answer 1 · 2017-06-02T09:14:59

#= 4a^3b^10#

In Algebra it is easier if you write a division as a fraction:

#((2a^2b^3)^4)/(4a^5b^2)" "larr#remove the bracket

Law of indices: #(x^my^n)^p = x^(mp)y^(np)#
Power to a power - multiply the indices.

#((2a^2b^3)^4)/(4a^5b^2) = (2^4a^8b^12)/(4a^5b^2)#

#=(16a^8b^12)/(4a^5b^2)" "larr# simplify the numbers

#=(4a^8b^12)/(a^5b^2)" "larr# subtract the indices

#= 4a^3b^10#