Answer
$\log_7{\left(\frac{x^8}{\sqrt[3]{y}}\right)}$
Work Step by Step
RECALL:
(1) $\log_b{m} - \log_b{n} = \log_b{(\frac{m}{n})}$
(2) $\log_b{m} + \log_b{n} = \log_b{(mn)}$
(3) $n \cdot \log_b{m} = \log_b{(m^n)}$
Use rule (3) above to obtain:
$=\log_7{(x^8)} - \log_7{(y^{\frac{1}{3}})}$
Use rule (1) above to obtain:
$=\log_7{\left(\frac{x^8}{y^{\frac{1}{3}}}\right)}$
Use the rule $a^{\frac{1}{3}} = \sqrt[3]{a}$ to obtain:
$=\log_7{\left(\frac{x^8}{\sqrt[3]{y}}\right)}$
