Question

Can someone walk me through the first two question in detail. My textbook doesn’t explain how to solve this.

Answer 1

see boxed results below

Explanation:

You want to simplify the sums of the given rational expressions.

Rules of exponents

The relevant rules of exponents are ...

(a^b)(a^c) = a^(b+c)

(a^b)/(a^c) = a^(b-c)

a^-b = 1/a^b

Application of these can be tedious, but is not difficult. We generally choose to write these expressions on one line with the variables in alphabetical order. Terms with like constellations of variables can be combined.

13.

`(p^2x^4)/(m^5)-(2p^4m^5)/(x^(-4))-(3p^2x^2)/(x^(-2)m^5)+(7p^2m^(-5)m^(10)x^4)/(p^(-2))\\\\\\=m^(-5)p^2x^4-2m^5p^4x^4-3m^(-5)p^2x^4+7m^5p^4x^4\\\\\\=5m^5p^4x^4-2m^(-5)p^2x^4=\boxed{5m^5p^4x^4-(2p^2x^4)/(m^5)}`

The 1st and 3rd terms were combined, as were the 2nd and 4th.

14.

`-(m^4x^5)/(k^5)+(2m^2x^5)/(k^5m^(-2))-(3m^3x^2k)/(m^(-4)x^3k^4)\\\\\\=-k^(-5)m^4x^5+2k^(-5)m^4x^5-3k^(-3)m^7x^(-1)\\\\\\=k^(-5)m^4x^5-3k^(-3)m^7x^(-1)=\boxed{(m^4x^5)/(k^5)-(3m^7)/(k^3x)}`

The first and second terms were combined.

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Additional comment

The attachment shows the simplification performed by a calculator. These are written in decreasing order of degree of the terms. (The degree is the sum of the exponents.)

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