Consider the following example. \[ 3 x^{2 / 3}=3 \sqrt[3]{x^{2}} \] Write the following in radical form. \[ x^{6 / 5} \]
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Did you know that radical notation can often simplify the visuals of complex expressions? The term \( x^{6/5} \) can be expressed in radical form as \( \sqrt[5]{x^6} \), which might look neater and make it easier to perform further operations like addition or multiplication with other radical expressions! If you're diving deeper into radical expressions, a common pitfall is forgetting about the base when simplifying. It's easy to overlook that \( x^{6/5} \) implies \( x \) raised to a power that can be split into a radical and an exponent! So remember: \( x^{6/5} = x^{1} \cdot x^{1/5} = x \cdot \sqrt[5]{x^1} \). Balancing clarity and simplicity makes all the difference!
