Chapter8: Roots And Radicals
Section8.5: Divide Radical Expressions
Problem 285E: Explain why multiplying 2x3 by its conjugate results in an expression with no radicals.
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
12.
![**Problem to Solve:**
Simplify \( \sqrt[3]{x^4 y^5} \).
**Solution:**
To simplify the expression \( \sqrt[3]{x^4 y^5} \), we use the property of radicals that allows us to distribute the radical over the product of the variables:
\[ \sqrt[3]{x^4 y^5} = \sqrt[3]{x^4} \cdot \sqrt[3]{y^5} \]
Next, we apply the rule \( \sqrt[3]{a^b} = a^{b/3} \):
\[ \sqrt[3]{x^4} = x^{4/3} \]
\[ \sqrt[3]{y^5} = y^{5/3} \]
Combining these, we get:
\[ \sqrt[3]{x^4 y^5} = x^{4/3} \cdot y^{5/3} \]
Therefore, the simplified form of \( \sqrt[3]{x^4 y^5} \) is:
\[ x^{4/3} y^{5/3} \]
**Final Answer:**
\[ x^{4/3} y^{5/3} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa93e090a-9cbe-4d28-ad82-733e885b8dfc%2F7467088b-7878-46c6-97e9-9594e8f76215%2F6bkdu6_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem to Solve:**
Simplify \( \sqrt[3]{x^4 y^5} \).
**Solution:**
To simplify the expression \( \sqrt[3]{x^4 y^5} \), we use the property of radicals that allows us to distribute the radical over the product of the variables:
\[ \sqrt[3]{x^4 y^5} = \sqrt[3]{x^4} \cdot \sqrt[3]{y^5} \]
Next, we apply the rule \( \sqrt[3]{a^b} = a^{b/3} \):
\[ \sqrt[3]{x^4} = x^{4/3} \]
\[ \sqrt[3]{y^5} = y^{5/3} \]
Combining these, we get:
\[ \sqrt[3]{x^4 y^5} = x^{4/3} \cdot y^{5/3} \]
Therefore, the simplified form of \( \sqrt[3]{x^4 y^5} \) is:
\[ x^{4/3} y^{5/3} \]
**Final Answer:**
\[ x^{4/3} y^{5/3} \]
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