If in the expression c=12a⁴/b, where a and b are doubled, then for equality to hold, one must

To maintain equality in the expression c = 12a⁴ / b when both a and b are doubled, we need to ensure that the resulting expression on both sides of the equation remains the same. Let's double both a and b: a' = 2a b' = 2b Now, we substitute the new values into the expression: c' = 12(a')⁴ / b' = 12(2a)⁴ / (2b) = 12 * 2⁴ * a⁴ / (2b) = 12 * 16 * a⁴ / (2b) = 192 * a⁴ / (2b) = 96 * a⁴ / b To maintain equality, c' must be equal to c: c' = c 96 * a⁴ / b = c Since the value of c remains the same after doubling both a and b, we can conclude that one must multiply the original expression by a factor of 96 to maintain equality.