As practice, “simplify” all of these expressions: rewrite them in a tidier form, without parenthesis if possible, with strictly positive exponents if it looks nice, and with a minimal number of terms/characters. You can check your answer by testing the initial expression and your result at some simple values of the variables to ensure they’re equal.
\(\displaystyle (3x)^5 \)
\(\displaystyle (7xy)^2(y) \)
\(\displaystyle (6x^2b^7)^3 \)
\(\displaystyle \bigl(7x^3-11x\bigr)\bigl(x^2+1\bigr) \)
\(\displaystyle \bigl(5x^5+2x^2\bigr)^2 \)
\(\displaystyle \bigl(1-x^2\bigr)\bigl(1-x-x^2\bigr) \)
\(\displaystyle \bigl(3\sqrt{y}+10z^7\bigr)^2 \)
\(\displaystyle \bigl(3a^{0.5}b^{-3}\bigr)^2 \)
\(\displaystyle \bigl(2u^{\tfrac{1}{2}}\sqrt[3]{r}\bigr)^{-7} \)
\(\displaystyle \bigl(\tfrac{1}{4}z^{-11}\sqrt[5]{v^2}q^{1.4}\bigr)^{3/2} \)
\(\displaystyle \frac{3x^5}{x^2} \)
\(\displaystyle \frac{5y^{-3}}{25y^8} \)
\(\displaystyle \biggl(\frac{7x^2y}{2xy^6}\biggr)^3 \)
\(\displaystyle \biggl(\frac{2s^7t}{t^2s}\biggr)^{-1} \)
\(\displaystyle \biggl(\frac{u-2}{u^2+1}\biggr)^{2} \)
\(\displaystyle \sqrt{\frac{3x^4z}{12z^{19}}} \)
\(\displaystyle \biggl(\frac{7x^2y}{2xy^6} + \frac{3}{(xy)^2} \biggr)^2 \)