Sure, let's solve the mathematical expression step-by-step.
The first step is to understand the expression we have. It's: `10` to the power of `log base 10 of 16`.
Step 1: Calculate the logarithm base 10 of 16.
By definition of the logarithm, log base 10 of a number x is the power to which 10 must be raised to get the number x. So, we need to find a power that will make 10 equal to 16. Using log rules or a calculator, we would find that `log10(16)` is approximately 1.20412.
Step 2: Now, we need to calculate 10 to the power of the result we just found.
This means we'll be calculating `10^1.20412`.
Since any number raised to the power of its logarithm (in the same base) equals the original number itself (because they are inverse operations just like multiplication and division or addition and subtraction), the result of 10^1.20412 is 16.
So, `k` equals to `16.0`.
Thus, the value of the given mathematical expression 10ˡᵒᵍ¹⁶ is `16.0`.