What is the solution to the equation 3√(4x³) * (4th root of x⁶) = 48?

To solve the equation ( 3\sqrt{(4x^3)} \cdot (\text{4th root of } x^6) = 48 ), we start by simplifying each term.

The term ( 3\sqrt{(4x^3)} ) can be rewritten as ( 3 \cdot 2\sqrt{x^3} = 6\sqrt{x^3} ) since ( \sqrt{4} = 2 ). This gives us:

[

6\sqrt{x^3} = 6x^{3/2}

]

Next, we handle the second term, the fourth root of ( x^6 ), which can be expressed as:

[

\text{4th root of } x^6 = x^{6/4} = x^{3/2}

]

Now, we can combine these two parts:

[

6x^{3/2} \cdot x^{3/2} = 6x^{3/2 + 3/2} = 6x^{3}

]

Thus, the equation becomes:

[

6x^{3} = 48

]

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