Respuesta :
Answer:
The powers of a,b and c for the given expression
[tex]\frac{(a^{-5}b^7c^3)^2}{(a^4b^{-2}c^2)^3}=a^{-22}b^{20}c^0}[/tex] is -22,20 and 0 respectively
Step-by-step explanation:
Given expression is [tex]\frac{(a^{-5}b^7c^3)^2}{(a^4b^{-2}c^2)^3}[/tex]
To find the powers of a,b and c:
[tex]\frac{(a^{-5}b^7c^3)^2}{(a^4b^{-2}c^2)^3}=\frac{(a^{-5})^2(b^7)^2(c^3)^2}{(a^4)^3(b^{-2})^3(c^2)^3}[/tex] ( using the property [tex](ab)^m=a^m.b^m[/tex] )
[tex]=\frac{a^{-10}b^{14}c^6}{a^{12}b^{-6}c^6}[/tex] ( using the property [tex](a^m)^n=a^{mn}[/tex] )
[tex]=a^{-10}b^{14}c^6.a^{-12}b^{6}c^{-6}[/tex] ( using the property [tex]\frac{1}{a^m}=a^{-m}[/tex] )
[tex]=a^{-10-12}b^{14+6}c^{6-6}[/tex] ( using the property [tex]a^m.a^n=a^{m+n}[/tex] )
[tex]=a^{-22}b^{20}c^{0}[/tex]
Therefore[tex]\frac{(a^{-5}b^7c^3)^2}{(a^4b^{-2}c^2)^3}=a^{-22}b^{20}c^{0}[/tex]
The powers of a,b and c for the given expression
[tex]\frac{(a^{-5}b^7c^3)^2}{(a^4b^{-2}c^2)^3}=a^{-22}b^{20}c^0}[/tex] is -22,20 and 0 respectively
