# Question Video: Simplifying and Solving Equations Involving πth Roots Mathematics

Find the value (or values) of π₯ if 12π₯β΅ = 384.

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### Video Transcript

Find the value, or values, of π₯ if 12π₯ to the fifth power equals 384.

Weβre going to solve this equation for π₯ by performing a series of inverse operations. We notice that π₯ to the fifth power is being multiplied by 12. So weβre going to begin by dividing both sides of this equation by 12. 384 divided by 12 is 32. So we get π₯ to the fifth power equals 32. Then, to solve this equation, we recall what we know about even and odd roots. Specifically, given the equation π¦ to the πth power equals π₯, if π is odd, then there is exactly one solution to this equation, π¦ equals the πth root of π₯.

Now, since our equation is in terms of π₯, weβre going to rewrite this slightly. So if π₯ to the πth power equals π¦, then π₯ is equal to the πth root of π¦. Now, in this case, π is odd; itβs equal to five. And so there is just one solution to this equation. Itβs π₯ equals the fifth root of 32. But of course, the fifth root of 32 is simply equal to two. And so, the solution is π₯ equals two.