Question

(17)^ 3 *(289)^ -6 =(17)^ 2m - 1​

Answer 1

m = -4

Explanation:

The given expression is :

`(17)^(3)\cdot(289)^(-6)=(17)^(2m-1)`

We need to find the value of m

We know that, 17² = 289

So,

`(17)^(3)\cdot(17^2)^(-6)=(17)^(2m-1)\\\\(17)^(3)\cdot(17)^(-12)=(17)^(2m-1)`

Also,
`x^ax^b=x^(a+b)`

So,

`17^(3-12)=17^(2m-1)\\\\17^(-9)=17^(2m-1)\\\\\implies -9=2m-1\\\\-9+1=2m\\\\-8=2m\\\\m=-4`

So, the value of m is equal to -4.