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y^2 X y^3 = y^(2 + 3) = y^5
You can only do this if the coefficient 'y' is the same for both terms.
Remember
y^2 = y X y
y^3 = y X y X y
Hence
y^2 X y^3 = y X y X y X y X y = y^5
Similarly for division/subtraction
y^3 / y^2 = y^(3 - 2 ) = y^1 = y The power of '1' is trivial and not normally shown.
NB You CANNOT do z^2 X y^3 by adding the indices.
z^2 X y^3 is (z^2)*(y^3)
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Area is notated as Unit squared because you are only dealing with 2 dimension (Length and Width). Volume, however, is unit cubed because you are now involving height as a third dimension.
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In mathematics, the expression 2xy represents the product of the number 2 and the variables x and y. This expression is known as a monomial, specifically a binomial because it consists of two terms. When simplified, 2xy cannot be further reduced unless additional information about the variables x and y is provided.
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The total squared error between the predicted y values and the actual y values
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The Mean Squared Error (MSE) is a measure of how close a fitted line is to data points. For every data point, you take the distance vertically from the point to the corresponding y value on the curve fit, this is known as the error, and square the value. Next you add up all those values for all data points, and divide by the number of points. The reason for squaring is so negative values do not cancel positive values. The smaller the Mean Squared Error, the closer the fit is to the data. The MSE has the units squared of whatever is plotted on the vertical axis.
What is the difference between 3 squared and 3 cubed?
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You have to put your heart into it!
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(x + y)(x + y)(x + y)
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It is y^2 or y squared
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x cubed y cubed z squared
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Their product.
