Question

Describe how to transform:

Answer 1

Answer:

$x^\frac{35}{6}$

Step-by-step explanation:

The expression to transform is:

$(\sqrt[6]{x^5})^7$

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:

$\sqrt[n]{a} = a^{\frac{1}{n}}$

Therefore $\sqrt[6]{a} = a^{\frac{1}{6}}$

Now let's replace $a$ with $x^{5}$ which is the algebraic form we are given inside the 6th root:

$\sqrt[6]{x^5} = (x^5)^{\frac{1}{6}}$

Now use the property that tells us how to proceed when we have  "exponent of an exponent":

$(a^n)^m= a^{n*m}$

Therefore we get:  $(x^5)^{\frac{1}{6}}=x^{\frac{5}{6}}}$

Finally remember that this expression was raised to the power 7, therefore:

$[tex](\sqrt[6]{x^5})^7=(x^\frac{5}{6})^7=x^\frac{35}{6}$[/tex]

An use again the property for the exponent of a exponent: