Question - Simplified Algebraic Expression with Fractions and Exponents
Solution:
The image contains an algebraic expression within a square root and two fractions added together underneath. Both the numerator and denominator of the fractions contain terms with x raised to powers and multiplied by y, and y multiplied by x raised to powers respectively.To solve or simplify the expression, let's consider each fraction separately and observe if there's a common pattern.Starting with the first fraction: `x^(2x-3y) / x^(3y-2x)`.We can simplify this using the laws of exponents. When we divide two exponents with the same base, we subtract the exponent in the denominator from the exponent in the numerator: `x^(a)/x^(b) = x^(a-b)`.Applying this law to the first fraction, we have:`x^(2x-3y - (3y-2x)) = x^((2x-3y) - 3y + 2x) = x^(4x-6y)`.For the second fraction `y^(2x-3y) / y^(3y-2x)`, the same rules apply:`y^(2x-3y - (3y-2x)) = y^((2x-3y) - 3y + 2x) = y^(4x-6y)`.Now adding the two simplified terms together:`x^(4x-6y) + y^(4x-6y)`.Under the square root, the expression cannot be simplified further algebraically without knowing the values of x and y. If x and y are equal, then we could factor out `(4x-6y)` as a common term, but since the expression doesn't provide that information, this is the simplest form.Therefore, the simplified form of the expression under the square root is:`sqrt(x^(4x-6y) + y^(4x-6y))`.And that's the expression simplified while using the "undefined" language code as required.
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