# Video: Evaluating Algebraic Expressions Using Laws of Exponents

Given that 7^(π₯) = 4, find the value of 7^(π₯ β 1).

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### Video Transcript

Given that seven to the π₯ power equals four, find the value of seven to the π₯ minus one power.

We know that seven to the π₯ power equals four. And weβre trying to solve seven to the π₯ minus one power. In order to solve this, weβll need to see if we can rewrite seven to the π₯ minus one power. And to do that, weβll have to remember some properties of exponents, like this one. π₯ to the π plus π power is equal to π₯ to the π power times π₯ to the π power, which means we can take seven to the π₯ minus one power and write it as seven to the π₯ power times seven to the negative one power.

We know that seven to the π₯ power equals four. And we also know π₯ to the negative π power is equal to one over π₯ to the π 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 π₯ power equals four, the value of seven to the π₯ minus one power is four over seven.