Questions: Simplify √[5]27 x^2 · √[5]9 x^3

Solution Steps

To simplify the expression $\sqrt[5]{27 x^{2}} \cdot \sqrt[5]{9 x^{3}}$, we can combine the two radicals by multiplying the terms inside the radicals and then simplifying the result.

Given the Python output, we have \(3 \cdot (x^2)^{\frac{1}{5}} \cdot (x^3)^{\frac{1}{5}}\).

Simplify the exponents: \((x^2)^{\frac{1}{5}} = x^{2 \cdot \frac{1}{5}} = x^{0.4}\) and \((x^3)^{\frac{1}{5}} = x^{3 \cdot \frac{1}{5}} = x^{0.6}\).

Substitute the simplified exponents back into the expression: \(3 \cdot x^{0.4} \cdot x^{0.6} = 3 \cdot x^{0.4 + 0.6} = 3x^1 = 3x\).

Final Answer