Essay: Show all work. A school designer wants to create a white board with the ptimal dimensions to enhance if one side of the white board x^-5xy+8y inches. Write an algebra expression for the area of the area of the area of such a white board, simplify it, and correct units with your solution.

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To find the area of the whiteboard, we need to multiply its length by its width. According to the given information, one side of the whiteboard is x^-5xy + 8y inches.

Let's assume that the other side of the whiteboard is represented by 'w' inches.

Therefore, the algebraic expression for the area of the whiteboard can be written as:
Area = (x^-5xy + 8y) * w

To simplify this expression, we can use the distributive property of multiplication over addition.

Area = x^-5xy * w + 8y * w

Next, we can simplify further by applying the power rule for exponents. According to the power rule, when we raise a variable with an exponent by another exponent, we multiply the exponents.

Area = x^-5xy * w + 8yw

Now, it's important to note that x^-5 represents 1/x^5. Therefore, we can rewrite x^-5xy as xy/x^5.

Area = (xy/x^5) * w + 8yw

To ensure the units are correct, we multiply the lengths in inches. Therefore, the unit of the area will be square inches.

So, the final expression for the area of the whiteboard is:
Area = (xy/x^5)w + 8yw square inches.

Remember, it's always helpful to check with your teacher or professor for any specific instructions they may have provided.