Microcode is far more low level than "to exponentiate, multiply repeatedly". More like, take an instruction such as ADD AX, BX. I'm using a 16-bit example to keep things simple. That might decode into micro-ops as follows:

1. set the ALU input 0 to take input from register AX

2. set the ALU input 1 to take input from register BX

3. set the ALU output to register AX

4. tell the ALU to ADD

And I bet I oversimplified it and got it wrong.

Each micro-op tells the CPU which control lines to turn on and off to activate the registers, ALU, memory bus, etc. Historically it lived on ROM for Intel parts, but that's changed in recent decades. User-programmable microcode was a thing; microcode extensions allowed the Xerox Alto's CPU to function as a proto-GPU, with operations like fast line draws and BitBlt, allowing the Smalltalk UI to be drawn MUCH faster than you'd expect a mid-70s minicomputer to do. Even in the micro era, the DEC Alpha and the Nintendo 64's GPU both had user-loadable microcode. Intel and AMD chips don't allow this; their microcode updates have to be vendor-signed.

But yeah, if you don't trust microcode, don't run an Intel CPU. Stick with God's own perfect CPU, the 6502... its control logic is hardwired, not microcoded. That's part of why it was so cheap and so fast.