Simplify \( \frac{-4 \sqrt{7} \times \sqrt{15}}{\sqrt{6}} \) and rationalize the denominator of the result.

A town has a population of 16000 and grows at \( 4.5 \% \) every year. What will be the population after 8 years, to the nearest whole number?

Use the properties of logarithms to expand the following expression. \[ \log \left(\frac{x^{3}}{\sqrt{(x+6)^{3}}}\right) \] Your answer should not have radicals or exponents. You may assume that all variables are positive. \( \log \left(\frac{x^{3}}{(x+6)^{3}}\right)=\square \)

AUTOEVALUACION Opera. \[ (-3)^{-2}+\left(\frac{3}{4}\right)^{-1}-2^{-3}\left(1-\frac{1}{2}\right)^{-2} \]

19. Эcenreruse: \( \frac{4^{0.5}}{0,5^{4}}= \) A) 4 Б) 8 B) 16 D) 32 D) 64

Complete the conjecture that describes the pattern in the sequence. \( 4,8,12,16,20 \)