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Rewrite the expression $\frac{{m}x^2+{n}x+{p}}{(x+a)(x+b)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+C$.

Rewrite the expression $\frac{mx+a}{nx+b}$ as partial fractions in the form $A+\frac{B}{nx+b}$.

Rewrite the expression $\frac{x+a}{x+b}$ as partial fractions in the form $A+\frac{B}{x+b}$.

Simplifying an expression of the form $\frac{a^4b^3}{\sqrt{a^4b^2}}$ to $a^2b^2$, for integers $a$ and $b$.

Simplifying an expression of the form $a^3 \times (a^4)^{1/2}$ to $a^5$, where $a$ is an integer. 

Using indices rules to rewrite an expression from $\left(\frac{a^n}{b^n}\right)^{-1/n}$ to $\frac{b}{a}$.

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $\frac{1}{b}$, for integers $a$, $b$, $m$ and $n$.

Simplifying expressions from $\frac{x^mx^n}{x^p}$ to $x^{m+n-p}$. 

Simplifying expressions from $\left(\frac{x^m}{x^n}\right)^p$ to $x^{(m-n)p}$.

Simplifying expressions from $(ax^n)^m$ to $a^mx^{mn}$, where $a$, $m$ and $n$ are positive integers.