It's your turn on exponential functions

Do your best in trying to solve the following problems. In any case some of them are solved in the video and all of them are solved in the pdf file below.

Exercise 1.

Draw the graph of (left(dfrac13right)^x) from that of (3^x).

Exercise 2.

Write each of the following expressions as a fraction without common factors: [81^{-frac{1}{4}},, 25^{-frac{3}{2}},, left(frac{16}{81}right)^{-1.25}.]

Exercise 3.

Find for which values of (xinmathbb R) the following expressions have a meaning: [2^{2x^2+5x},, left(frac{1}{2}right)^{sqrt{x}}, (x-1)^{pi}+(3-x)^{-frac{1}{2}}+5^{sqrt{x+1}}.]