Question

What value of `a` will make `((12x^a)/(4x^5))^3 = 27x^12`?

Answer 1

To find `a` we have to perform `((12x^a)/(4x^5))^3` by applying some power properties then solve the given equation.
`" "`
`color(blue)(((12x^a)/(4x^5))^3`
`"`
`=(12x^a)^3/(4x^5)^3`
`" "`
`=(12^3xx(x^a)^3)/(4^3xx(x^5)^3`
`" "`
`=(1728xxx^(3a))/(64xxx^15)`
`" "`
`=1728/64xxx^(3a)/x^15`
`" "`
`color(blue)(=27xxx^(3a-15)`
`"`
Now let us solve the given equation:
`" "`
`((12x^a)/(4x^5))^3=27x^12`
`" "`
`rArrcolor(blue)(cancel27xxx^(3a-15))=cancel27x^12`
`" "`
`rArrx^(3a-15)=x^12`
`" "`
`rArr3a-15=12`
`" "`
`rArr3a=12+15`
`" "`
`rArr3a=27rArra=27/3`
`" "`
Therefore,`" "a=9`

Answer 2

`a=9`

Explanation:

`((12x^a)/(4x^5))^3 =27 x^12` Multiplying by `(4x^5)^3` in both sides

we get , `(12x^a)^3 =27*x^12 *64*x^15` or

`12^3 x^(3a) = 27*64* x^27 or x^(3a)= 27*64*x^27/12^3`or

`x^(3a) = x^27 :. 3a =27 or a =9` [Ans]