IDNLearn.com: Your trusted platform for finding reliable answers. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.
Sagot :
Sure, let's break this down step-by-step:
First, we start with the expression [tex]\(\sqrt[7]{x} \cdot \sqrt[7]{x} \cdot \sqrt[7]{x}\)[/tex].
1. Express each term using exponents:
[tex]\[ \sqrt[7]{x} = x^{\frac{1}{7}} \][/tex]
Thus, our expression [tex]\(\sqrt[7]{x} \cdot \sqrt[7]{x} \cdot \sqrt[7]{x}\)[/tex] can be written as:
[tex]\[ x^{\frac{1}{7}} \cdot x^{\frac{1}{7}} \cdot x^{\frac{1}{7}} \][/tex]
2. Combine the exponents:
When we multiply terms with the same base, we add the exponents. We have:
[tex]\[ x^{\frac{1}{7}} \cdot x^{\frac{1}{7}} \cdot x^{\frac{1}{7}} = x^{\left(\frac{1}{7} + \frac{1}{7} + \frac{1}{7}\right)} \][/tex]
3. Add the exponents:
[tex]\[ \frac{1}{7} + \frac{1}{7} + \frac{1}{7} = \frac{3}{7} \][/tex]
4. Write the final expression:
[tex]\[ x^{\frac{3}{7}} \][/tex]
So, the simplified form of [tex]\(\sqrt[7]{x} \cdot \sqrt[7]{x} \cdot \sqrt[7]{x}\)[/tex] is [tex]\(\boxed{x^{\frac{3}{7}}}\)[/tex].
First, we start with the expression [tex]\(\sqrt[7]{x} \cdot \sqrt[7]{x} \cdot \sqrt[7]{x}\)[/tex].
1. Express each term using exponents:
[tex]\[ \sqrt[7]{x} = x^{\frac{1}{7}} \][/tex]
Thus, our expression [tex]\(\sqrt[7]{x} \cdot \sqrt[7]{x} \cdot \sqrt[7]{x}\)[/tex] can be written as:
[tex]\[ x^{\frac{1}{7}} \cdot x^{\frac{1}{7}} \cdot x^{\frac{1}{7}} \][/tex]
2. Combine the exponents:
When we multiply terms with the same base, we add the exponents. We have:
[tex]\[ x^{\frac{1}{7}} \cdot x^{\frac{1}{7}} \cdot x^{\frac{1}{7}} = x^{\left(\frac{1}{7} + \frac{1}{7} + \frac{1}{7}\right)} \][/tex]
3. Add the exponents:
[tex]\[ \frac{1}{7} + \frac{1}{7} + \frac{1}{7} = \frac{3}{7} \][/tex]
4. Write the final expression:
[tex]\[ x^{\frac{3}{7}} \][/tex]
So, the simplified form of [tex]\(\sqrt[7]{x} \cdot \sqrt[7]{x} \cdot \sqrt[7]{x}\)[/tex] is [tex]\(\boxed{x^{\frac{3}{7}}}\)[/tex].
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com is your go-to source for accurate answers. Thanks for stopping by, and come back for more helpful information.