Final answer:
The expression (5x^4y^3)^(2/9) in radical form is the 9th root of (25x^8y^6) or √[25x^8y^6] when simplified according to the rules of exponents.
Step-by-step explanation:
The expression provided, (5x^4y^3)^(2/9), can be simplified using the rules of exponents. To express it in radical form, we must recognize that a fractional exponent corresponds to a root. The numerator of the fraction is the power to which the inside of the radical is raised, and the denominator is the index of the root, the type of root being taken.
So, taking the expression (5x^4y^3)^(2/9), we have a radical with an index of 9 and each term inside is raised to the 2nd power:
√[5^2(x^4)^2(y^3)^2]
which simplifies to √[25x^8y^6]. Now we express it with a ninth root symbol, which finalizes our expression as 9th root of (25x^8y^6), or in radical notation: √[25x^8y^6].
In mathematical operations and equilibriums, the ability to convert between exponents and roots is essential for simplifying expressions and solving equations. Always remember to apply exponents to all terms inside parentheses and simplify wherever possible.