Question

(17)^ 3 *(289)^ -6 =(17)^ 2m - 1​

Answer 1

Answer:

m = -4

Step-by-step 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.