Using a p-value of .05 for each test is extremely misleading because you haven't taken into account the fact that you are doing repeated tests. If you incorrectly use a p-value of .05 for each test, you will often incorrectly report statistically significant results. One way to avoid this problem is to specify an overall p-value for all tests, usually .05, and divide this by the number of tests. If any of the 20 tests has a p-value below .0025, you can confidently say the results are statistically significant. If you've done a statistical test and found it statistically significant, there is no need to worry about power.
Power is the probability of finding a statistically significant difference.
It is based on the sample size and the alternative hypothesis. You use power when designing a study. If the study has a power of .9 for a given sample size and alternative hypothesis, it means there is .9 probability of finding a statistically significant result with that sample size and alternative hypothesis. On the other hand, if you do not find statistical significance, then someone might wonder if your study had low power. Questions about power often arise because the p-value does not provide all the information of interest.