Answer:
[tex]x^\frac{35}{6}[/tex]
Step-by-step explanation:
The expression to transform is:
[tex](\sqrt[6]{x^5})^7[/tex]
Let's work first on the inside of the parenthesis.
Recall that the n-root of an expression can be written as a fractional exponent of the expression as follows:
[tex]\sqrt[n]{a} = a^{\frac{1}{n}}[/tex]
Therefore [tex]\sqrt[6]{a} = a^{\frac{1}{6}}[/tex]
Now let's replace [tex]a[/tex] with [tex]x^{5}[/tex] which is the algebraic form we are given inside the 6th root:
[tex]\sqrt[6]{x^5} = (x^5)^{\frac{1}{6}}[/tex]
Now use the property that tells us how to proceed when we have "exponent of an exponent":
[tex](a^n)^m= a^{n*m}[/tex]
Therefore we get: [tex](x^5)^{\frac{1}{6}}=x^{\frac{5}{6}}}[/tex]
Finally remember that this expression was raised to the power 7, therefore:
[tex][tex](\sqrt[6]{x^5})^7=(x^\frac{5}{6})^7=x^\frac{35}{6}[/tex][/tex]
An use again the property for the exponent of a exponent:
