Solve: 5x^(3/4)- 15 = 0.

Question

Accepted Answer

Welcome back. I'm so glad you're here. We get to solve this equation four X to the 3/ minus 12 equals zero. So we want to get X by itself. Going to zoom through the first couple steps here. So adding 12 to both sides. We've got four X to the 3/5 equals a positive 12, dividing both sides by four. And on the left we've got X to the 3/ equals and on the right three. Okay now what do we do? We've got X raised to a fraction. So what we're going to do for this exponent to get rid of the exponents When it's a fraction we're going to raise it to another fraction because when you have a an exponent raised to an exponent they get multiplied. And so we're going to multiply it by multiply it by and raise it to simultaneously five thirds 3/5 times five thirds is one. So the left hand side is going to be X to the first or just X. But it's a very important that what we do to one side we do to the other. So we need to raise three to the five thirds as well. So we now have X equals three to the five thirds. Well, excess by itself. That's great. Now let's just work on simplifying the right hand side of the equation three to the five thirds. As you recall from previous lessons the when we have an exponents, that is a fraction. The denominator of that exponent fraction is going to be the root of our radical. So the denominator down low part that's the root and that leaves us with three inside the radical. And it's going to be raised to our numerator from the fraction exponents. So it's going to be three to the fifth. The numerator up high. So that remains our exponent. So now we can do some simplification. We recall from previous lessons that three to the fifth is the same as three to the third times three squared. So we've still got the third root of that three to the third times three squared. Well when we're taking the cubed root of three to the third that is just going to be three leaving inside of our radical. The cubed root of three squared and our last bit of simplification. Three times the cubed root Of three square that is nine. So we've got three times the cubed root of nine. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one

Solve: 5x^(3/4)- 15 = 0.

Key Concepts

Exponents and Fractional Powers

Isolating Variables

Roots and Their Properties

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