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24X^5Y^8/30X^3Y^10

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1 Answer

It's not very clear, but I'm assuming that problem looks like the following:

     (24·x5·y8)/(30·x3·y10)

First, notice that 6 is a factor of both the coefficients in the numerator and the denominator. So the expression can be reduced as follows:

     (6·4·x5·y8)/(6·5·x3·y10) = (4·x5·y8)/(5·x3·y10)

When dividing exponents with like bases, we keep the same base and subtract the smaller exponent from the larger exponent. For instance, 

     x5/x3 = x5-3/x3-3 = x2/x0 = x2/1 = x2

     y8/y10 = y8-8/y10-8 = y0/y2 = 1/y2

Therefore,

     (4·x5·y8)/(5·x3·y10) = (4·x5-3·y8-8)/(5·x3-3·y10-8)

                             = (4·x2·y0)/(5·x0·y2)

                             = (4·x2·1)/(5·1·y2)

                             = (4·x2)/(5·y2)

Thus,

     (24x5y8)/(30x3y10) = (4x2)/(5y2)

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