How do you simplify #\frac { 75b ^ { 5} c ^ { 2} } { - 15b ^ { 8} c ^ { - 15} }#?

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Answer 1 · 2018-03-09T23:29:46

#color(blue)(-5b^(-3)c^(17)#

Given:

#\frac { 75b ^ { 5} c ^ { 2} } { - 15b ^ { 8} c ^ { - 15} }#

We will group the like terms as shown below:

#color(red)[-(75/15)(b^5/b^8)(c^2/{c^(-15)})# Expression.1

Formula used:

#color(green)(a^m * a^n = a^(m+n)#

#color(green)(a^m / a^n = a^(m-n)#

Simplify Expression.1 using the formula listed above:

#color(blue)[-(75/15)(b^5/b^8)(c^2/{c^(-15)})# Expression.1

#rArr -(75/15)(b^(5-8))(c^(2-color(green)((-15))})#

#rArr -cancel 75^color(red)( 5)/cancel(15)(b^(5-8))(c^(2+15))#

#rArr (-5)(b^(-3))(c^(17))#

#rArr color(blue)(-5b^(-3)c^(17)#