To solve the given expression
[tex]\[
4\left(\sqrt[5]{x^2 y}\right) + 3\left(\sqrt[5]{x^2 y}\right),
\][/tex]
follow these steps:
1. Identify the common term:
The term [tex]\(\sqrt[5]{x^2 y}\)[/tex] is common in both parts of the expression.
2. Factor out the common term:
[tex]\[
4\left(\sqrt[5]{x^2 y}\right) + 3\left(\sqrt[5]{x^2 y}\right) = (4 + 3)\left(\sqrt[5]{x^2 y}\right)
\][/tex]
3. Add the coefficients:
Simplify the expression inside the parentheses.
[tex]\[
4 + 3 = 7
\][/tex]
So the expression becomes:
[tex]\[
7\left(\sqrt[5]{x^2 y}\right)
\][/tex]
4. Rewrite the final expression:
Rewriting the term [tex]\(\sqrt[5]{x^2 y}\)[/tex] using its exponent form gives:
[tex]\[
\sqrt[5]{x^2 y} = (x^2 y)^{1/5}
\][/tex]
5. Combine the results:
Substituting back, the final expression becomes:
[tex]\[
7 \left( \sqrt[5]{x^2 y} \right) = 7 \left( (x^2 y)^{1/5} \right)
\][/tex]
Thus, the simplified form of the given sum is:
[tex]\[
7\left( (x^2 y)^{1/5} \right) \quad \text{or} \quad 7 (x^2 y)^{0.2}
\][/tex]
