How did the evolution of science affect the evolution of technology?

The question is asking how scientific breakthroughs result in technological evolution.

It's correct that mostly scientific breakthroughs - the groundbreaking kinds - lead to what we consider ingenious technologies.

Examples are when our understanding of electromagnetic waves expanded to our understanding radio waves and what we call x-rays (higher-energy radio waves). When we learned there exists a wave called an x-ray, which we can control, we found uses for them such as medical x-rays that could see through the body.

Similarly, when we learned about antimatter (specifically positrons), we learned to control them sufficiently that we could create a machine (technology) that generated PET scans - again for medical imaging.

And when we found a model for how atoms might be (the nucleus surrounded by spacially large electron shells), and we combined this with isotopes and the periodic table, we came up with ways to control nuclear fission (leading to current atomic power plants and atomic bombs). This, along with newer scientific knowledge of atomic fusion, later led to hydrogen bombs and hopefully fusion-based power plants.

We're now getting solid scientific knowledge of the types of genomes throughout the biological world, and with this we are able to create new and novel animals and plants, such as drought-resistant and insect-resistant crops or glowing insects (drosophila) and frogs. Though this area is very controversial and may become more so as we can create more complex and unique living beings (e.g. cows that give a fine wine variatal instead of milk, or a plant that has psychotropic properties without dependency risks).

Science mostly has and will continue to lead technological breakthroughs. However, sometimes a new technology (such as the computer, or microscopes) can lead to further scientific advances.