{"status": "success", "data": {"description_md": "**POTD February 15, 2024**\n\nLet $x, y \\in \\mathbb{Q}$ and $(3^{x+1})(6^{2x+y})(9^{4-x}) = \\frac{0.75^y}{27^{x-1}}$. If $x+y$ can be expressed as $-\\frac{a}{b}$, where $a$ and $b$ are relatively prime, positive integers, evaluate $a+b$.", "description_html": "<p><strong>POTD February 15, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">x, y \\in \\mathbb{Q}</span> and <span class=\"katex--inline\">(3^{x+1})(6^{2x+y})(9^{4-x}) = \\frac{0.75^y}{27^{x-1}}</span>. If <span class=\"katex--inline\">x+y</span> can be expressed as <span class=\"katex--inline\">-\\frac{a}{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are relatively prime, positive integers, evaluate <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Problem of the Day #70", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}