Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. \( \log _{\mathrm{b}}\left(\frac{x^{3} y}{z^{7}}\right) \)

Which expression is equivalent to \( 7^{\frac{2}{5}} \) ?

Write a recursive rule for the sequence. 23. \( 3,-1,-5,-9,-13, \ldots \)

Which expression is equivalent to \( \sqrt[4]{6^{2}} \) ? \( 66^{8} \) \( 6^{\frac{1}{2}} \)

Which expression is equivalent to \( \sqrt{5} \) ? \( 5^{\frac{1}{2}} 2^{5} \) \( 5^{\frac{1}{5}} \)

Example 1 The coed soccer team has four times as many boys on it as it has girls. We say the ratio of the number of number of girls on the team is \( 4: 1 \). We read this as four to one.