IMathAS-libretexts

Simplifying Expressions Mini-Lesson Review
The table below shows the steps that a student used to simplify three expressions. For each problem, identify the mistake (if it exists). Assume variables are nonzero numbers.
$\displaystyle {\left(\frac{{4}}{{5}}\right)}^{{-{{2}}}}$ $\displaystyle {\left(\frac{{5}}{{4}}\right)}^{{2}}$ $\displaystyle \frac{{5}^{{2}}}{{4}^{{2}}}$ $\displaystyle \frac{{25}}{{16}}$ All steps are correct	$\displaystyle \frac{{{3}{x}^{{3}}+{9}{x}-{12}}}{{{3}{x}}}$ $\displaystyle \frac{{{3}{x}^{{3}}}}{{{3}{x}}}+\frac{{{9}{x}}}{{{3}{x}}}-\frac{{12}}{{{3}{x}}}$ $\displaystyle {x}^{{2}}+{3}-{4}{x}$ $\displaystyle {x}^{{2}}-{4}{x}+{3}$ All steps are correct	$\displaystyle {\left({7}{a}^{{-{{2}}}}\right)}^{{-{{2}}}}$ $\displaystyle {\left({7}\right)}^{{-{{2}}}}{\left({a}^{{-{{2}}}}\right)}^{{-{{2}}}}$ $\displaystyle {7}^{{-{{2}}}}{a}^{{-{2}\cdot-{2}}}$ $\displaystyle -{49}{a}^{{4}}$ All steps are correct