91Ó°ÊÓ

In Exercises, write the logarithmic equation as an exponential equation, or vice versa. $$ \ln 2=0.6931 \ldots $$

In Exercises, find the slope of the tangent line to the exponential function at the point \((0,1)\).

In Exercises, use the properties of exponents to simplify the expression. (a) \(\left(e^{3}\right)\left(e^{4}\right)\) (b) \(\left(e^{3}\right)^{4}\) (c) \(\left(e^{3}\right)^{-2}\) (d) \(e^{0}\)

In Exercises, evaluate each expression. (a) \(5\left(5^{3}\right)\) (b) \(27^{2 / 3}\) (c) \(64^{3 / 4}\) (d) \(81^{1 / 2}\) (e) \(25^{3 / 2}\) (f) \(32^{2 / 5}\)

In Exercises, evaluate each expression. (a) \(\left(\frac{1}{5}\right)^{3}\) (b) \(\left(\frac{1}{8}\right)^{1 / 3}\) (c) \(64^{2 / 3}\) (d) \(\left(\frac{5}{8}\right)^{2}\) (e) \(100^{3 / 2}\) (f) \(4^{5 / 2}\)

In Exercises, use the properties of exponents to simplify the expression. (a) \(\left(\frac{1}{e}\right)^{-2}\) (b) \(\left(\frac{e^{5}}{e^{2}}\right)^{-1}\) (c) \(\frac{e^{5}}{e^{3}}\) (d) \(\frac{1}{e^{-3}}\)

In Exercises, write the logarithmic equation as an exponential equation, or vice versa. $$ \ln 9=2.1972 \ldots $$

In Exercises, find the slope of the tangent line to the exponential function at the point \((0,1)\).

In Exercises, find the slope of the tangent line to the exponential function at the point \((0,1)\).

In Exercises, write the logarithmic equation as an exponential equation, or vice versa. $$ \ln 0.2=-1.6094 \ldots $$