Question

question select the expression that is equivalent to (sqrt4{3} cdot sqrt5{3^{3}}).

Explanation:

Step1: Convert radicals to exponents

$\sqrt[4]{3} = 3^{\frac{1}{4}}$, $\sqrt[5]{3^3} = 3^{\frac{3}{5}}$

Step2: Multiply using exponent rule

When multiplying like bases, add exponents: $3^{\frac{1}{4}} \cdot 3^{\frac{3}{5}} = 3^{\frac{1}{4}+\frac{3}{5}}$

Step3: Add the fractions

Find common denominator (20): $\frac{1}{4}+\frac{3}{5} = \frac{5}{20}+\frac{12}{20} = \frac{17}{20}$

Step4: Convert back to radical form

$3^{\frac{17}{20}} = \sqrt[20]{3^{17}}$

Answer:

$\sqrt[20]{3^{17}}$ (or equivalently $3^{\frac{17}{20}}$)