Reciprocal of $7.5^{1-x}$

Question

Ok my calculator tells me the reciprocal of $7.5^{1-x}$ is $0.1333\cdot7.5^x$. Can anyone explain the steps involved to get this manually?

Is it along the line of the reciprocal of $7.5^1 + 7.5^{-x} = 0.13333 \cdot 7.5^{-x}$?

Answer 1

$$\frac{1}{7.5^{1-x}} = \frac{1}{7.5^{1}\cdot7.5^{-x}} = \frac{2}{15}\cdot7.5^{x} \approx 0.13333\cdot7.5^{x}$$

Answer 2

The reciprocal of$$7.5^{1-x}$$ is $$\frac 1{7.5^{1-x}}=\frac 1{7.5*7.5^{-x}}=\frac 1{7.5}*\frac 1{7.5^{-x}}=0.13333*7.5^x$$