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Power rule with rational exponents

A questionnaire was given to students. The first question asked was
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22. Use the exponent laws to simplify each expression. Leave your answers with positive exponents.\newlinea) (x3)(x−23) \left(x^{3}\right)\left(x^{\frac{-2}{3}}\right) \newlineb) (81−0.25)3 \left(81^{-0.25}\right)^{3} \newlinec) (m−2)23(m12)4 \frac{\left(m^{-2}\right)^{\frac{2}{3}}}{\left(m^{\frac{1}{2}}\right)^{4}} \newlined) (9p2)−12(p−32) \left(9 p^{2}\right)^{-\frac{1}{2}}\left(p^{-\frac{3}{2}}\right) \newlinee) [x−2(xy)4]1.5 \left[\frac{x^{-2}}{(x y)^{4}}\right]^{1.5} \newlinef) [4x−29y−4]−52 \left[\frac{4 x^{-2}}{9 y^{-4}}\right]^{-\frac{5}{2}} \newline33. For each of the following, use the exponent laws to help identify a value for p p that satisfies the equation.\newlinea) (xp)13=x23 \left(x^{p}\right)^{\frac{1}{3}}=x^{\frac{2}{3}} \newlineb) (xp)(x34)=x2 \left(x^{p}\right)\left(x^{\frac{3}{4}}\right)=x^{2} \newlinec) xpx−2=x52 \frac{x^{p}}{x^{-2}}=x^{\frac{5}{2}} \newlined) (81−0.25)3 \left(81^{-0.25}\right)^{3} 00\newlinee) (81−0.25)3 \left(81^{-0.25}\right)^{3} 11\newlinef) (81−0.25)3 \left(81^{-0.25}\right)^{3} 22\newline44. Evaluate without using a calculator. Leave your answers as rational numbers.\newlinea) (81−0.25)3 \left(81^{-0.25}\right)^{3} 33\newlineb) (81−0.25)3 \left(81^{-0.25}\right)^{3} 44\newlinec) (81−0.25)3 \left(81^{-0.25}\right)^{3} 55\newlined) (81−0.25)3 \left(81^{-0.25}\right)^{3} 66\newlinee) (81−0.25)3 \left(81^{-0.25}\right)^{3} 77\newlinef) (81−0.25)3 \left(81^{-0.25}\right)^{3} 88\newline55. Evaluate using a calculator. Express your answers to four decimal places, if necessary.\newlinea) (81−0.25)3 \left(81^{-0.25}\right)^{3} \newlineb) (m−2)23(m12)4 \frac{\left(m^{-2}\right)^{\frac{2}{3}}}{\left(m^{\frac{1}{2}}\right)^{4}} 00\newlined) (m−2)23(m12)4 \frac{\left(m^{-2}\right)^{\frac{2}{3}}}{\left(m^{\frac{1}{2}}\right)^{4}} 11\newlinee) (m−2)23(m12)4 \frac{\left(m^{-2}\right)^{\frac{2}{3}}}{\left(m^{\frac{1}{2}}\right)^{4}} 22\newlinec) (m−2)23(m12)4 \frac{\left(m^{-2}\right)^{\frac{2}{3}}}{\left(m^{\frac{1}{2}}\right)^{4}} 33\newlinef) (m−2)23(m12)4 \frac{\left(m^{-2}\right)^{\frac{2}{3}}}{\left(m^{\frac{1}{2}}\right)^{4}} 44
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Student Login | Get More Math!\newlineEdison High / Homepage\newlinet.html\newline77\newline77\newline77\newline77 of 1212\newlinePONTS\newlinePOWTS\newlineTOOAY\newlineTHISWEEX\newlineEAVE\newlineApril 99 Slope\newlineChange Assignment\newlineCREDTS\newliner\newline$ \$ \newlineFirst try was incorrect\newlineFind the slope of the line that passes through the following points:\newline(−3,6)(0,−6) \begin{array}{l} (-3,6) \\ (0,-6) \end{array} \newlineYx \frac{Y}{x} \newlinex2 x^{2} \newlinef(x) f(x) \newlinexn \sqrt[n]{x} \newlinexn x_{n} \newline✓ \checkmark \newline(x) (x) \newline∣x∣ |x| \newline≤ \leq \newlineYx \frac{Y}{x} 00\newlineYx \frac{Y}{x} 11\newlineUndefined\newlineYx \frac{Y}{x} 22\newlineskill code: 301024301024
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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3x+3f(x) = 3x + 3\newlineg(x)=−3x2g(x) = -3x^2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
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