(^7�ã2x^6y)^11 can you explain to me how to rewrite this rational exponent
Certainly! To rewrite the rational exponent, let's break it down step by step.
First, let's look at the base, which is the expression inside the parentheses: (2x^6y).
Next, let's consider the exponent, which is 11/7. To understand how to handle this rational exponent, we can think of it as a fraction. The numerator, 11, represents the power to which the base should be raised, and the denominator, 7, represents the root to be taken.
Now, in order to simplify the expression, we can distribute the exponent of 11/7 to each term inside the parentheses.
Starting with 2, we raise it to the power of 11/7: 2^(11/7).
Similarly, for x^6, we raise it to the power of 11/7: (x^6)^(11/7).
Finally, for y, we raise it to the power of 11/7: y^(11/7).
To write the entire expression with the rational exponent simplified, we combine the results above:
(2^(11/7))(x^((6*(11/7))))(y^(11/7)).
To further simplify, we can perform the necessary exponent operations:
2^(11/7) cannot be simplified further because the base is a number.
(x^((6*(11/7)))) simplifies to x^(66/7) by multiplying the exponents.
y^(11/7) cannot be simplified further because the base is a variable.
So, the final simplified expression is:
(2^(11/7))(x^(66/7))(y^(11/7)).