Question

select the expression that is equivalent to \\(sqrt4{2^3} cdot sqrt3{2}\\).

Explanation:

Step1: Convert radicals to exponents

$\sqrt[4]{2^3} = 2^{\frac{3}{4}}$, $\sqrt[3]{2} = 2^{\frac{1}{3}}$

Step2: Multiply using exponent rule

When multiplying like bases, add exponents: $2^{\frac{3}{4}} \cdot 2^{\frac{1}{3}} = 2^{\frac{3}{4}+\frac{1}{3}}$

Step3: Add the fractions

Find common denominator (12): $\frac{3}{4}+\frac{1}{3} = \frac{9}{12}+\frac{4}{12} = \frac{13}{12}$

Step4: Convert back to radical form

$2^{\frac{13}{12}} = \sqrt[12]{2^{13}} = \sqrt[12]{2^{12} \cdot 2} = 2\sqrt[12]{2}$

Answer:

$2\sqrt[12]{2}$ (or equivalently $\sqrt[12]{2^{13}}$)