Questions: The radical expression √[7](x^6) can be rewritten in the rational exponent form x^(a/b) where, a= b=

Solution Steps

To rewrite the radical expression \(\sqrt[7]{x^{6}}\) in rational exponent form, we use the property that \(\sqrt[n]{x^m} = x^{\frac{m}{n}}\). Here, \(m = 6\) and \(n = 7\), so the expression becomes \(x^{\frac{6}{7}}\).

The given radical expression is \(\sqrt[7]{x^{6}}\). To convert this into rational exponent form, we apply the property of exponents that states \(\sqrt[n]{x^m} = x^{\frac{m}{n}}\).

In our expression, we have:

• \(m = 6\)
• \(n = 7\)

Using the identified values, we can express the radical as: \[ \sqrt[7]{x^{6}} = x^{\frac{6}{7}} \]

Final Answer