Power consumption in Arithmetic Operation in Arduino UNO
The power consumed by the chip won't change much by multiplying (compared to, say, adding). The chip is always fetching and executing instructions, unless you have put it into one of its sleep modes.

The only power consumption change would be if the instruction had a side-effect on a peripheral. For example, turning on the ADC unit (for analog reading), or by setting an output pin high or low.

Having said that, I set up a couple of tests and measured the power consumption. I didn't use a Uno because the power used by the "power on" LED and the voltage regulator tend to swamp the power consumption of the chip itself. However it was tested on an Atmega328P.



Addition

Test sketch

volatile int foo = 100;
int main (void)
  {
  DDRB = 0b00111111;  // all ports to output
  DDRC = 0b00111111;
  DDRD = 0b11111111;
  PORTB = 0;          // write LOW
  PORTC = 0;
  PORTD = 0;

  while (true)
    foo += 42;
  }


Generated code

  a6:   80 91 00 01     lds r24, 0x0100
  aa:   90 91 01 01     lds r25, 0x0101
  ae:   8a 96           adiw    r24, 0x2a   ; 42
  b0:   90 93 01 01     sts 0x0101, r25
  b4:   80 93 00 01     sts 0x0100, r24
  b8:   f6 cf           rjmp    .-20        ; 0xa6 &lt;main+0x10&gt;


Measured consumption

I measured an average of 7.00 mA.



Multiplication

Test sketch

volatile int foo = 100;
int main (void)
  {
  DDRB = 0b00111111;  // all ports to output
  DDRC = 0b00111111;
  DDRD = 0b11111111;
  PORTB = 0;          // write LOW
  PORTC = 0;
  PORTD = 0;

  while (true)
    foo *= 42;
  }


Generated code

  a6:   4a e2           ldi r20, 0x2A   ; 42
  a8:   20 91 00 01     lds r18, 0x0100
  ac:   30 91 01 01     lds r19, 0x0101
  b0:   42 9f           mul r20, r18
  b2:   c0 01           movw    r24, r0
  b4:   43 9f           mul r20, r19
  b6:   90 0d           add r25, r0
  b8:   11 24           eor r1, r1
  ba:   90 93 01 01     sts 0x0101, r25
  be:   80 93 00 01     sts 0x0100, r24
  c2:   f2 cf           rjmp    .-28        ; 0xa8 &lt;main+0x12&gt;


Measured consumption

I measured an average of 6.32 mA.



Conclusion

I found this rather surprising, that it used less power doing a multiplication compared to an addition. Setting all ports to output and low was intended to remove any side-effects from spurious inputs on the input ports.

Still, as you can see from the generated code, most of the instructions are "helper" instructions (like loading from registers, storing to registers, looping etc.).

I'm still not sure I believe the results, perhaps someone else would like to try to reproduce them?

Update

As Edgar Bonet pointed out, the multiplication test became zero after 14 iterations and thus it gave the processor the simpler task of multiplying by zero. I changed the multiplier to 41 which does not become zero. This time the average consumption was 7.34 mA which was higher than the addition test.