OG详解-OG6 数学2 Q20

The correct answer is 724​​. An expression of the form ⁿ√am​, where m and n are integers greater than 1 and a ≥0, is equivalent to am​n​ . Therefore, the expression on the right-hand side of the given equation, ³√47​ , is equivalent to 47​3​ . Thus, 4^8c = 47​3​.   It follows that 8c = 73​​ . Dividing both sides of this equation by 8 yields c = 7​24​. Note that 7/24, .2916, .2917, 0.219, and 0.292 are examples of ways to enter a correct answer.