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

Answer:

The simplified form is $x^{\frac{4}{9}}=\sqrt[9]{x^4}$

Step-by-step explanation:

We are given,

The expression is of the form $\sqrt[9]{x}\times \sqrt[9]{x}\times \sqrt[9]{x}\times \sqrt[9]{x}$.

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

Now, upon simplifying, we have,

$\sqrt[9]{x}\times \sqrt[9]{x}\times \sqrt[9]{x}\times \sqrt[9]{x}\\\\=x^{\frac{1}{9}}\times x^{\frac{1}{9}}\times x^{\frac{1}{9}}\times x^{\frac{1}{9}}$

Since, $a^x\times a^y=a^{x+y}$. We get,

$x^{\frac{1}{9}}\times x^{\frac{1}{9}}\times x^{\frac{1}{9}}\times x^{\frac{1}{9}}\\\\=x^{\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}}\\\\=x^{\frac{4}{9}}\\\\=\sqrt[9]{x^4}$

Thus, the simplified form is $x^{\frac{4}{9}}=\sqrt[9]{x^4}$