Question

Find the missing term (x^12)^5 x (x^-2)^9 x what =(x^40)^5

Answer 1

The missing term is x^158

Explanation:

Let A denote the missing term.

`(x^(12))^5 \cdot (x^(-2))^9 \cdot A =(x^(40))^5\\x^(60)\cdot x^(-18)\cdot A = x^(200)\\x^(42)\cdot A = x^(200)\\A = x^(200)\cdot x^(-42)=x^(158)`

Answer 2

`x^(158)`

Explanation:

We are given,

`(x^(12) )^(5) * (x^(-2) )^(9) * y = (x^(40) )^(5)`.

It is required to find the value of y.

Now, on simplifying above equation, we get,

`x^(60) * x^(-18) * y = x^(200)`

i.e.
`x^(42) * y = x^(200)`

i.e.
`y = x^(200) * x^(-42)`

i.e.
`y = x^(158)`

Hence, the missing term is
`x^(158)`.