Questions: Which of the following is equivalent to (3^(1/4))^7 ?

Solution Steps

To solve the expression \((\sqrt[4]{3})^{7}\), we can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\). Here, \(\sqrt[4]{3}\) can be rewritten as \(3^{1/4}\). Therefore, the expression becomes \((3^{1/4})^7\), which simplifies to \(3^{(1/4) \cdot 7}\).

The original expression is \((\sqrt[4]{3})^{7}\). We can rewrite \(\sqrt[4]{3}\) as \(3^{1/4}\). Therefore, the expression becomes \((3^{1/4})^7\).

Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify \((3^{1/4})^7\) to \(3^{(1/4) \cdot 7}\).

Calculate the exponent: \((1/4) \cdot 7 = 1.75\). Thus, the expression simplifies to \(3^{1.75}\).

Calculate \(3^{1.75}\) to find the equivalent value. The result is approximately \(6.839\).

Final Answer