You're taking the verse out of context. Jesus didn't give believers power to trample snakes and scorpions. We haven't been given power or authority from Jesus. That was given to his 72 disciples. Here's the entire passage:

(Luke 10:1-20 NIV) After this the Lord appointed seventy-two others and sent them two by two ahead of him to every town and place where he was about to go. {2} He told them, "The harvest is plentiful, but the workers are few. Ask the Lord of the harvest, therefore, to send out workers into his harvest field. {3} Go! I am sending you out like lambs among wolves. {4} Do not take a purse or bag or sandals; and do not greet anyone on the road. {5} "When you enter a house, first say, 'Peace to this house.' {6} If a man of peace is there, your peace will rest on him; if not, it will return to you. {7} Stay in that house, eating and drinking whatever they give you, for the worker deserves his wages. Do not move around from house to house. {8} "When you enter a town and are welcomed, eat what is set before you. {9} Heal the sick who are there and tell them, 'The kingdom of God is near you.' {10} But when you enter a town and are not welcomed, go into its streets and say, {11} 'Even the dust of your town that sticks to our feet we wipe off against you. Yet be sure of this: The kingdom of God is near.' {12} I tell you, it will be more bearable on that day for Sodom than for that town. {13} "Woe to you, Korazin! Woe to you, Bethsaida! For if the miracles that were performed in you had been performed in Tyre and Sidon, they would have repented long ago, sitting in sackcloth and ashes. {14} But it will be more bearable for Tyre and Sidon at the judgment than for you. {15} And you, Capernaum, will you be lifted up to the skies? No, you will go down to the depths. {16} "He who listens to you listens to me; he who rejects you rejects me; but he who rejects me rejects him who sent me." {17} The seventy-two returned with joy and said, "Lord, even the demons submit to us in your name." {18} He replied, "I saw Satan fall like lightning from heaven. {19} I have given you authority to trample on snakes and scorpions and to overcome all the power of the enemy; nothing will harm you. {20} However, do not rejoice that the spirits submit to you, but rejoice that your names are written in heaven."