simplify the expression
(the 7th root of 11x/y^6)(the 7th root of y^6/11x^8)
the root is over the whole fraction in both cases.
I've already done the problem once and got x(the 7th root of 1/x). which apparently this is wrong.
when multiplying roots, take the root of the product. You then have
7throot( (11x/y^6) * (y^6/11x^8) )
= 7throot(1/x^7)
= 1/x
It would help if you showed your work...
thanks next time i'll show my work. you've been a big help.
To simplify the given expression, let's start by simplifying each individual root separately.
First, let's simplify the 7th root of 11x/y^6:
To simplify the 7th root of 11x/y^6, we can rewrite it as (11x/y^6)^(1/7), where the exponent 1/7 represents taking the 7th root.
Next, let's simplify the 7th root of y^6/11x^8:
To simplify the 7th root of y^6/11x^8, we can rewrite it as (y^6/11x^8)^(1/7).
Now that we have rewritten both roots, we can simplify the expression by multiplying the two roots together:
[(11x/y^6)^(1/7)] * [(y^6/11x^8)^(1/7)]
To multiply two roots together, we can combine the two fractions inside the roots:
(11x * y^6) / (11x^8 * y^6)^(1/7)
Now, let's simplify the expression inside the second root by multiplying the exponents of the variables:
(11x * y^6) / [(11x^8 * y^6)^(1/7)]
Using the property of exponents, we can rewrite the expression as:
(11x * y^6) / (11^(1/7) * x^(8/7) * y^(6/7))
Now, simplify further by multiplying the constants outside the root:
(11 * x * y^6) / (11^(1/7) * x^(8/7) * y^(6/7))
To simplify the expression, combine the variables with the same base by subtracting their exponents:
11^(1-8/7) * x^(1-8/7) * y^(6-6/7)
11^(-1/7) * x^(-1/7) * y^(36/7 - 6/7)
Finally, simplify the expression:
1 / (11^(1/7) * x^(1/7) * y^(1/7))
Therefore, the simplified expression is 1 / (11^(1/7) * x^(1/7) * y^(1/7)).