20. Vereinfache im Kopf. \( \begin{array}{lll}\text { a) }\left(5^{\frac{4}{5}}\right)^{\frac{5}{2}} & \text { b) }\left(36^{\frac{3}{4}}\right)^{\frac{2}{3}} & \text { c) }\left(49^{-\frac{6}{7}}\right)^{\frac{7}{12}}\end{array} \)

Using the change of base formula, express \( \log_{2}(8) \) in terms of common logarithm.

3 Consider the product \( \left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right) \ldots \) Each factor in the product is of the form \( \left(1+\frac{1}{n}\right) \) for \( n \geq 2 \). Determine ALL the values of \( n \) for which the product will be an integer value.

What is the absolute value of \( 2-i \) ? A. 2 B. \( \sqrt{3} \) C. \( \sqrt{5} \) D. \( 2+i \) E. \( -2+i \)

Simplify the expression without using a calculator. \( \ln e^{2}=\square \)

Find \( \|\mathbf{v}\| \). \( \mathbf{v}=-3 \mathbf{i}+7 \mathbf{j} \) \( \begin{array}{l}\|\mathbf{v}\|=\square \\ \text { (Simplify your answer. Type an exact answer, using radicals as needed.) }\end{array} \)