Respuesta :
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:
The simplified form is [tex]x^{\frac{4}{9}}=\sqrt[9]{x^4}[/tex]
Step-by-step explanation:
We are given,
The expression is of the form [tex]\sqrt[9]{x}\times \sqrt[9]{x}\times \sqrt[9]{x}\times \sqrt[9]{x}[/tex].
It is required to find the simplified form of the expression.
Now, upon simplifying, we have,
[tex]\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}}[/tex]
Since, [tex]a^x\times a^y=a^{x+y}[/tex]. We get,
[tex]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}[/tex]
Thus, the simplified form is [tex]x^{\frac{4}{9}}=\sqrt[9]{x^4}[/tex]
