answer:First, let's simplify the right side of the equation. We have sqrt[8]{16} = sqrt[8]{2^4} = sqrt{2}. So the equation becomes sqrt{Q^3} = 16sqrt{2}. Next, we can square both sides of the equation to eliminate the square root. This gives us Q^3 = (16sqrt{2})^2 = 256 cdot 2 = 512. To solve for Q, we take the cube root of both sides of the equation. This gives us Q = sqrt[3]{512} = boxed{8}. The answer is: 8

answer:First, we multiply 15 by 7/10: 15 times frac{7}{10} = frac{15 times 7}{10} = frac{105}{10}. Next, we multiply the result by 1/9: frac{105}{10} times frac{1}{9} = frac{105 times 1}{10 times 9} = frac{105}{90}. Simplifying the fraction, we find that frac{105}{90} reduces to frac{7}{6}. Therefore, the value of the expression is boxed{frac{7}{6}}. The answer is: frac{7}{6}

answer:Substituting x = 2 and y = 1 into the expression 2times x - 3 times y, we get [2 times 2 - 3 times 1 = 4 - 3 = boxed{1}.] The answer is: 1

answer:We are given that the operation x , Diamond , y satisfies the equations (xy) , Diamond , y=x(y , Diamond , y) and (x , Diamond , 1) , Diamond , x = x , Diamond , 1 for all x,y>0. We are also given that 1 , Diamond , 1=1. To find X , Diamond , 98, we can use the given equations and properties of the operation to simplify the expression. Using the first equation, we have: 1 cdot 98 , Diamond , 98 = 1 cdot (98 , Diamond , 98) 98 , Diamond , 98 = 98 , Diamond , 98 This tells us that 98 , Diamond , 98 is equal to itself. Using the second equation, we have: (X , Diamond , 1) , Diamond , X = X , Diamond , 1 Plugging in the value X , Diamond , 98 for (X , Diamond , 1), we have: (X , Diamond , 98) , Diamond , X = X , Diamond , 1 Now, we can substitute the value 1 , Diamond , 1 = 1 into the equation to simplify it further: (X , Diamond , 98) , Diamond , X = X Since 98 , Diamond , 98 is equal to itself, we can rewrite the equation as: 98 , Diamond , X = X Given that 98 , Diamond , X = 19, we can substitute this value into the equation: 19 = X The value of X is 19. The answer is: 19