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Given the area of a circle is [tex]$\pi r^2[tex]$[/tex], express the area of the circle with radius [tex]$[/tex]2xy^2$[/tex] as a monomial.

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GinnyAnswer
To find the area of a circle where the radius is given in a specific form, follow these steps:

1. Identify the formula for the area of a circle: The area of a circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle.

2. Substitute the given radius into the formula: In this problem, the radius \( r \) is given as \( 2xy^2 \).

3. Substitute \( 2xy^2 \) for \( r \) in the area formula:
[tex]\[ A = \pi (2xy^2)^2 \][/tex]

4. Simplify the expression inside the parentheses first:
[tex]\[ (2xy^2)^2 = (2xy^2) \times (2xy^2) \][/tex]

5. Use the properties of exponents to expand this multiplication:
[tex]\[ (2xy^2) \times (2xy^2) = 2^2 \times x^2 \times (y^2)^2 \][/tex]

6. Calculate the powers:
[tex]\[ 2^2 = 4 \quad \text{and} \quad (y^2)^2 = y^{2 \times 2} = y^4 \][/tex]
Hence, it becomes:
[tex]\[ (2xy^2)^2 = 4x^2y^4 \][/tex]

7. Substitute this result back into the area formula:
[tex]\[ A = \pi \times 4x^2y^4 \][/tex]

8. Multiply the constants and keep the \( \pi \) factor:
[tex]\[ A = 4\pi x^2 y^4 \][/tex]

Therefore, the area of the circle with radius \( 2xy^2 \) expressed as a monomial is:
[tex]\[ A = 4\pi x^2 y^4 \][/tex]
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