Final answer:
The given equation x = 4y²/5z² can be simplified by aligning it with the principles of exponent manipulation and recognizing square roots as fractional powers if necessary. The specific 'standard form' required is not mentioned, which leaves the equation reduction incomplete without that critical piece of information.
Step-by-step explanation:
The equation x = 4y²/5z² needs to be simplified to one of the standard forms. To do this, we simplify the equation into its most basic terms. The denominator can be simplified if it represents a perfect square.
One approach would be to consider the fractional exponents, as suggested by the reference to Equation A.8 and re-expression of square roots as fractional powers. In that example, the square root of x could be expressed as x² = √x. This knowledge of exponents and square roots will help in simplifying the equation further.
However, without additional context on what the 'standard forms' refer to in this question, we cannot provide a specific solution. In general, standard forms can refer to linear equations, polynomials, conics, or other mathematical expressions placed in a particular structure for simplicity and ease of analysis.