Simplify the following index question?

#(5m^4p^2)/(2m^3p)divide(5m^2p^6)^3/(3m^7p)#

1 Answer
Jim G.
Jul 23, 2017

#(3m^2)/(50p^(16)#

Explanation:

#"using the "color(blue)"laws of indices"#

#•color(white)(x)(a^mb^n)^p=a^((mp))b^((np))#

#•color(white)(x)a^mxxa^n=a^((m+n))#

#•color(white)(x)a^m/a^nhArra^((m-n))" or "1/ a^((n-m))#

#"we can express division of fractions as multiplication"#

#rArra/b-:c/d=a/bxxd/c#

#rArr(5m^4p^2)/(2m^3p)xx(3m^7p)/(125m^6p^(18))#

#=(15m^(11)p^3)/(250m^9p^(19)#

#=(3m^2)/(50p^(16))larrcolor(red)" with positive indices"#

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