Video: Evaluating Algebraic Expressions Using Laws of Exponents

Given that 7^(π‘₯) = 4, find the value of 7^(π‘₯ βˆ’ 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 we’re trying to solve seven to the π‘₯ minus one power. In order to solve this, we’ll need to see if we can rewrite seven to the π‘₯ minus one power. And to do that, we’ll have to remember some properties of exponents, like this one. π‘₯ to the π‘Ž plus 𝑏 power is equal to π‘₯ to the π‘Ž power times π‘₯ to the 𝑏 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‘Ž power is equal to one over π‘₯ to the π‘Ž 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.

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