第9章平方根と根号

Population growth The expression $10·x^n$ models the growth of a mold population after $n$ generations. There were 10 spores at the start, and each had $x$ offspring. So $10·x^5$ is the number of offspring at the fifth generation. At the fifth generation there were 10,240 offspring. Simplify the expression $\sqrt[5]{\frac{\mathrm{10,240}}{10}}$ to determine the number of offspring of each spore.

Spread of a virus The expression $3·x^n$ models the spread of a virus after $n$ cycles. There were three people originally infected with the virus, and each of them infected $x$ people. So $3·x^4$ is the number of people infected on the fourth cycle. At the fourth cycle 1875 people were infected. Simplify the expression $\sqrt[4]{\frac{1875}{3}}$ to determine the number of people each person infected.

Explain how you know that $\sqrt[5]{x^{10}}=x^2$ .

Explain why $\sqrt[4]{\mathrm{-64}}$ is not a real number but $\sqrt[3]{\mathrm{-64}}$ is.