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olasank [31]
4 years ago
7

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

Mathematics
2 answers:
Ksivusya [100]4 years ago
6 0
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).
faltersainse [42]4 years ago
3 0

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}

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