Solve for x: ∛(x√x) = 9

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Hello. Today we're going to be solving the following equation. So the equation given to us is the cube root of X times the square root of X equal to 20. Now. In order to start solving this equation, we need to go ahead and isolate the argument inside of the cube root. In order to do that. We can take the third power of the entire equation. Doing so is going to cancel out the cuBA on the left hand side of the equation. Leaving us with X times the square of X. And on the right hand side we are left with 20 raised to the third power. Now 20 raised to the third power is going to give us the value of 8000 and we can go ahead and combine X times the square root of X. Using exponential multiplication in order to do that. We can go ahead and rewrite the square root of X as X to the half power. So doing so is going to give us x times x rays to the half power. And we can go ahead and perform exponential multiplication which will allow us to rewrite this as X raised to the power of one plus one half. And that's going to give us X raised to the 3/2 power. Now we can go ahead and rewrite this one more time as a square root. And this is going to give us the square root of X to the third power. So the left hand side of the equation can be rewritten as the square root of X to the third equal to 8000. Now, once again, we want to go ahead and isolate this X cubed quantity so we can go ahead and square both sides of the equation. Doing so is going to leave us with x cubed on the left hand side of the equation. And 8000 race to the second power, which is going to give us 64 million. And finally we want to go ahead and get rid of this cubic exponent. So we can take the cube root of the entire equation. Doing so is going to leave us with just X on the left hand side and the Cube root of 64 million, which is going to be 400. And that is going to be the solution to our equation. And that means that the answer to this problem is going to be D. So I hope this video helps you in understanding how to solve this type of equation. And I'll go ahead and see you all in the next video.

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