Introduction:
The given expression is 1÷a^loga to the base b. In order to find its value, we need to understand some basic concepts of logarithms and exponentials.

Logarithms and Exponentials:
Logarithms and exponentials are inverse functions of each other. The logarithm of a number to a given base is the power to which the base must be raised to produce that number. On the other hand, the exponential of a number is the result of raising the base to the power of that number.

Solution:
We can rewrite the given expression as follows:

1÷a^loga to the base b = 1÷(b^logb to the base a)^loga to the base b

Now, we can use the property of logarithms which states that logb to the base a = 1÷loga to the base b. Therefore, we can rewrite the expression as:

1÷(b^logb to the base a)^(1÷loga to the base b)

Next, we use the property of exponents which states that (a^b)^c = a^(b*c). Therefore, we can simplify the expression as follows:

1÷b^(logb to the base a*(1÷loga to the base b))

Now, we can use the property of logarithms again to simplify the expression further. We know that loga to the base a = 1, so we can rewrite the expression as:

1÷b^(1*1÷loga to the base b) = 1÷b^(1÷loga to the base b)

Final Answer:
Therefore, the value of 1÷a^loga to the base b is 1÷b^(1÷loga to the base b).