Question

(a^(-5)b^(7)c^(3))^(2)-:(a^(4)b^(-2)c^(2))^(3) What are the powers of a b and c

Answer 1

The powers of a,b and c for the given expression

`((a^(-5)b^7c^3)^2)/((a^4b^(-2)c^2)^3)=a^(-22)b^(20)c^0}` is -22,20 and 0 respectively

Explanation:

Given expression is
`((a^(-5)b^7c^3)^2)/((a^4b^(-2)c^2)^3)`

To find the powers of a,b and c:

`((a^(-5)b^7c^3)^2)/((a^4b^(-2)c^2)^3)=((a^(-5))^2(b^7)^2(c^3)^2)/((a^4)^3(b^(-2))^3(c^2)^3)` ( using the property
`(ab)^m=a^m.b^m` )

`=(a^(-10)b^(14)c^6)/(a^(12)b^(-6)c^6)` ( using the property
`(a^m)^n=a^(mn)` )

`=a^(-10)b^(14)c^6.a^(-12)b^(6)c^(-6)` ( using the property
`(1)/(a^m)=a^(-m)` )

`=a^(-10-12)b^(14+6)c^(6-6)` ( using the property
`a^m.a^n=a^(m+n)` )

`=a^(-22)b^(20)c^(0)`

Therefore
`((a^(-5)b^7c^3)^2)/((a^4b^(-2)c^2)^3)=a^(-22)b^(20)c^(0)`

The powers of a,b and c for the given expression

`((a^(-5)b^7c^3)^2)/((a^4b^(-2)c^2)^3)=a^(-22)b^(20)c^0}` is -22,20 and 0 respectively