Question

What is the value of k in the product of powers below?

welp

Answer 1

I guess : k = -1 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 2

Answer: The required value of k is -1.

Step-by-step explanation: We are given to find the value of k in the product of the following powers :

`10^(-3).10.10^k=10^(-3)~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We will be using the following properties of exponents to solve the given equation.

`(i)~a^b.a^c=a^(b+c),\\\\(ii)~a^x=a^y~~~~\Rightarrow x=y.`

From equation (i) we have

`10^(-3).10.10^k=10^(-3)\\\\\Rightarrow 10^(-3+1+k)=10^(-3)\\\\\Rightarrow 10^(-2+k)=10^(-3)\\\\\Rightarrow -2+k=-3\\\\\Rightarrow k=-3+2\\\\\Rightarrow k=-1`

Therefore, the required value of k is -1.