Question

What is the simplified form of the ninth root of x times the ninth root of x times the ninth root of x times the ninth root of x

Answer 1

Since you are working with exponents and roots you would add the exponents together. The ninth root of x is equal to x^(1/9) and since you are using it four times your answer would be x^(4/9).

Answer 2

The simplified form is
`x^{(4)/(9)}=\sqrt[9]{x^4}`

Explanation:

We are given,

The expression is of the form
`\sqrt[9]{x}* \sqrt[9]{x}* \sqrt[9]{x}* \sqrt[9]{x}`.

It is required to find the simplified form of the expression.

Now, upon simplifying, we have,

`\sqrt[9]{x}* \sqrt[9]{x}* \sqrt[9]{x}* \sqrt[9]{x}\\\\=x^{(1)/(9)}* x^{(1)/(9)}* x^{(1)/(9)}* x^{(1)/(9)}`

Since,
`a^x* a^y=a^(x+y)`. We get,

`x^{(1)/(9)}* x^{(1)/(9)}* x^{(1)/(9)}* x^{(1)/(9)}\\\\=x^{(1)/(9)+(1)/(9)+(1)/(9)+(1)/(9)}\\\\=x^{(4)/(9)}\\\\=\sqrt[9]{x^4}`

Thus, the simplified form is
`x^{(4)/(9)}=\sqrt[9]{x^4}`