Video Transcript
Given that seven to the 𝑥 power equals four, find the value of seven to the 𝑥 minus one power.
We know that seven to the 𝑥 power equals four. And we’re trying to solve seven to the 𝑥 minus one power. In order to solve this, we’ll need to see if we can rewrite seven to the 𝑥 minus one power. And to do that, we’ll have to remember some properties of exponents, like this one. 𝑥 to the 𝑎 plus 𝑏 power is equal to 𝑥 to the 𝑎 power times 𝑥 to the 𝑏 power, which means we can take seven to the 𝑥 minus one power and write it as seven to the 𝑥 power times seven to the negative one power.
We know that seven to the 𝑥 power equals four. And we also know 𝑥 to the negative 𝑎 power is equal to one over 𝑥 to the 𝑎 power. Which means we can rewrite seven to the negative one power as one over seven to the positive one power, which is just one-seventh. Four times one-seventh is four-sevenths. And so, we can say, given that seven to the 𝑥 power equals four, the value of seven to the 𝑥 minus one power is four over seven.
