Which expression is equivalent to V6x 3, Your answer: 6°xy 15,,18 O 6x5y5 1. 3,,6 O 6xy 31 5,5 65
Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
![### Simplifying Radical Expressions: An Example
**Question**: Which expression is equivalent to \(\sqrt[5]{6x^3y^6}\)?
**Options**:
1. \(6^5x^{15}y^{18}\)
2. \(6x^{\frac{3}{5}}y^{\frac{6}{5}}\)
3. \(6^{\frac{1}{5}}x^{3}y^{6}\)
4. \(6^{\frac{1}{5}}x^{\frac{3}{5}}y^{\frac{6}{5}}\)
**Explanation**:
To find an equivalent expression for the fifth root of the given expression, we can break down the problem step by step.
The given expression is \(\sqrt[5]{6x^3y^6}\).
Recall that the \(n\)-th root of a product can be written as the product of the \(n\)-th roots:
\[
\sqrt[5]{6x^3y^6} = 6^{\frac{1}{5}} (x^3)^{\frac{1}{5}} (y^6)^{\frac{1}{5}}
\]
Next, simplify each part individually:
1. \(6^{\frac{1}{5}}\)
2. \((x^3)^{\frac{1}{5}} = x^{\frac{3}{5}}\)
3. \((y^6)^{\frac{1}{5}} = y^{\frac{6}{5}}\)
Combining these, we get:
\[
6^{\frac{1}{5}} x^{\frac{3}{5}} y^{\frac{6}{5}}
\]
Thus, the equivalent expression is:
\[
6^{\frac{1}{5}} x^{\frac{3}{5}} y^{\frac{6}{5}}
\]
**Correct Option**:
The correct answer is the last option:
\[
\boxed{6^{\frac{1}{5}} x^{\frac{3}{5}} y^{\frac{6}{5}}}
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