Final answer:
The expression 2m^7 x n^-4 x p^-3 / 4m^-2 x n^6 x p^-5 simplifies to m^9 x n^-10 x p^2 when we apply the properties of exponents by subtracting the exponents in the denominator from those in the numerator for each base.
Step-by-step explanation:
The expression 2m^7 x n^-4 x p^-3 / 4m^-2 x n^6 x p^-5 can be simplified by using the properties of exponents. We can combine the terms with the same bases by subtracting the exponents of the terms in the denominator from those in the numerator.
Firstly, for the m terms: 2m^7 / 4m^-2 becomes 0.5m^(7 - (-2)) which simplifies to 0.5m^9. Similarly, for the n terms: n^-4 / n^6 becomes n^(-4 - 6), which simplifies to n^-10. Lastly, for the p terms: p^-3 / p^-5 becomes p^(-3 - (-5)) which simplifies to p^2.
Combining all the simplified terms, we get: 0.5m^9 x n^-10 x p^2. Since there is a coefficient of 0.5 for the m term, we can multiply through by 2 to get the final simplified expression: m^9 x n^-10 x p^2.