- #1
Paencake
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Quick math question: Why does 1/(x^4) = 4^4 simplify to 1/x = 4?
Paencake said:I don't understand why the exponents are disregarded.
Number Nine said:They're not. Take the fourth root of each side.
Number Nine said:They're not. Take the fourth root of each side.
symbolipoint said:[itex]\frac{1}{x^4}=(\frac{1}{x})^4[/itex]
[itex]\sqrt{(\frac{1}{x})^4}=\pm (\frac{1}{x})^2 [/itex]
[itex]\sqrt{(\frac{1}{x})^2}=\pm\frac{1}{x} [/itex]
dextercioby said:Fixed.
The equation 1/(x^4) = 4^4 simplifies to 1/x = 4 by taking the fourth root of both sides of the equation. This results in x^4 = 4, which can be further simplified to x = 4^(1/4) or x = 4^(1/4).
The equation simplifies to 1/x = 4 because the fourth root of 4^4 is 4, and when we take the fourth root of x^4, the x term is eliminated, leaving us with 1/x = 4.
No, the equation 1/(x^4) = 4^4 simplifies to 1/x = 4 and cannot be simplified further.
This equation has applications in various fields of science, such as physics and chemistry, where it can be used to calculate values related to energy and electric fields.
Yes, this equation can be solved for a specific value of x using algebraic methods. For example, if we substitute x = 4^(1/4) into the equation, we get 1/(4^(1/4))^4 = 4^4, which simplifies to 1/4 = 4^4. Therefore, x = 4^(1/4) is a valid solution to the equation.