Sums & Products: Sudoku for all the maths aficionados out there

Today's Video:

Excellent puzzle from a debut on this channel of StastiasticallyYes. I resorted to a calculator in the end 🙈

Link to Play:

Sums & Products by StatisticallyYes https://tinyurl.com/SudokuSleuthSumsAndProducts

Rules:

Normal sudoku rules apply: each row, column, and box must contain the digits 1 to 9 without repeats.

Shade some cells in the grid such that all shaded cells are orthogonally connected and all unshaded cells are orthogonally connected. Each cage is either fully shaded or fully unshaded.

For unshaded cages, the number in the corner is the sum of the digits in the cage. For shaded cages, the number is the product of the digits. Numbers cannot repeat in cages.