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.