Given that the cube root of 27 is 3. what is 27^(4)/(3) 12 108 81 3

To solve this problem, we need to understand the concept of fractional exponents and how they relate to roots and powers.<br /><br />The expression \(27^{\frac{4}{3}}\) can be broken down as follows:<br /><br />1. The cube root of 27 is 3, which means \(27^{\frac{1}{3}} = 3\).<br />2. We need to raise this result to the power of 4.<br /><br />So, we can rewrite the expression using the property of exponents:<br />\[ 27^{\frac{4}{3}} = (27^{\frac{1}{3}})^4 \]<br /><br />Since \(27^{\frac{1}{3}} = 3\), we have:<br />\[ (27^{\frac{1}{3}})^4 = 3^4 \]<br /><br />Now, calculate \(3^4\):<br />\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \]<br /><br />Therefore, the value of \(27^{\frac{4}{3}}\) is 81.<br /><br />So, the correct answer is:<br />\[ \boxed{81} \]