Question

23 write the exponential expression in radical form. 3x^\frac{3}{5} a 3^\frac{3}{5} \sqrt5{x^3} b 3 \sqrt3{x^5} c 3 \sqrt5{x^3} d \sqrt5{3x^3}

Explanation:

Step1: Recall Exponent-Radical Rule

The rule for converting an exponential expression \( a^{\frac{m}{n}} \) to radical form is \( \sqrt[n]{a^m} \) (or \( a^{\frac{m}{n}} = \sqrt[n]{a^m} \)). Also, for a product like \( 3x^{\frac{3}{5}} \), we apply the rule to the variable part.

Step2: Analyze the Given Expression

Assuming the original expression is \( 3x^{\frac{3}{5}} \) (since the options suggest a fractional exponent on \( x \)). Using the rule \( x^{\frac{m}{n}}=\sqrt[n]{x^m} \), for \( x^{\frac{3}{5}} \), \( n = 5 \) and \( m = 3 \), so \( x^{\frac{3}{5}}=\sqrt[5]{x^3} \). The coefficient 3 remains as is. So the expression \( 3x^{\frac{3}{5}} \) in radical form is \( 3\sqrt[5]{x^3} \), which matches option C.

Answer:

C. \( 3\sqrt[5]{x^3} \)