venus says that the quantity of 6m raise to 5 over 4 are equal to 6m 4th root of 6m?do you agree why or why not?
To determine whether the quantity 6m raised to the power of 5/4 is equal to 6m multiplied by the 4th root of 6m, we can compare the two expressions algebraically.
Let's first simplify and evaluate each expression separately:
Expression 1: (6m)^(5/4)
To evaluate this expression, we apply the exponent to the base:
(6m)^(5/4) = (6^1 * m^1)^(5/4) = 6^(5/4) * m^(5/4)
To simplify the exponent of 6, we can rewrite it as the square root of the square root:
6^(5/4) = (6^(1/2))^(5/2) = (√6)^(5/2)
So, the first expression becomes:
(6m)^(5/4) = (√6)^(5/2) * m^(5/4)
Expression 2: 6m * (6m)^(1/4)
To evaluate this expression, we apply the same method as before:
(6m)^(1/4) = 6^(1/4) * m^(1/4)
So, the second expression becomes:
6m * (6m)^(1/4) = 6m * (6^(1/4) * m^(1/4))
Now, let's compare the two expressions:
(6m)^(5/4) = (√6)^(5/2) * m^(5/4)
6m * (6m)^(1/4) = 6m * (6^(1/4) * m^(1/4))
At this point, we can see that the two expressions are not equivalent. The first expression involves taking the 5/2 power of the square root of 6, while the second expression only raises 6 to the 1/4 power.
Therefore, based on this algebraic comparison, we can conclude that the quantity (6m)^(5/4) is not equal to 6m multiplied by the 4th root of 6m.