How do you simplify #\frac { ( a^ { - 3} b ^ { - 1} e ^ { - 5} ) ^ { - 2} } { ( a ^ { 5} b ^ { 2} c ^ { 2} ) ^ { 5} }#?

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Answer 1 · 2017-07-21T03:12:10

#e^10/(a^19b^8c^10)#

Begin by applying the power rule for exponents: #(a^m)^n=a^(m*n)#

#(a^((-3*-2)) b^((-1*-2))e^((-5*-2)))/(a^((5*5)) b^((2*5)) c^((2*5)))#

#=(a^6b^2e^10)/(a^25b^10c^10)#

Apply the quotient rule for exponents: #(a^m)/a^n=a^(n-m)#

#(a^((6-25))b^((2-10))e^10)/c^10-> (a^-19b^-8e^10)/c^10#

Lastly, rewrite using positive exponents (if needed) by apply the negative exponent rule: #a^-n=1/a^n#

#(1/a^19 1/b^8 e^10)/c^10->e^10/(a^19b^8c^10) larr# Final answer