Question: (\left( \frac{1}{7} \right)^{-1} = 7^{-1}\)…

\(\left( \frac{1}{7} \right)^{-1} = 7^{-1}\)

Solution

The problem in the photo involves finding the missing number in the blank box such that: \[ \left( \frac{1}{7} \right)^{-1} = \Box \times 7^{-1} \] Step 1: Simplify \(\left( \frac{1}{7} \right)^{-1}\). The reciprocal of \(\frac{1}{7}\) is \(7\). Therefore: \[ \left( \frac{1}{7} \right)^{-1} = 7 \] Step 2: Simplify \(7^{-1}\). The reciprocal of \(7\) is \(\frac{1}{7}\). Therefore: \[ 7^{-1} = \frac{1}{7} \] Step 3: Set up the equation to find the missing number. \[ 7 = \Box \times \frac{1}{7} \] Step 4: Solve for the missing number. Multiply both sides by \(7\): \[ 7 \times 7 = \Box \] \[ 49 = \Box \] Therefore, the missing number is 49.