How to do exponential division when base and exponent is different between numerator and denominator?

Question

How to do division when

a ^x / b ^y

Say, a,x,b,y are distinct values.

For example,

2 ¹⁹ / 7 ²³ . Doing mathematical operations with bigger exponents is tedious and error-prone.

Is there any way to simplify above expression such that the final decimal result wouldn't change?

Answer 1

7 ²³ = 2 ^{23 log ₂ 7} .

2 ¹⁹ /2 ^{23 log ₂ 7} = 2 ^{19 - 23 log ₂ 7}