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Citrus2011 [14]
2 years ago
11

When 9 Superscript two-thirds is written in simplest radical form, which value remains under the radical?

Mathematics
2 answers:
salantis [7]2 years ago
9 0

Answer:

  3

Step-by-step explanation:

9^{\frac{2}{3}}=(3^2)^{\frac{2}{3}}=3^{\frac{4}{3}}=3\cdot 3^{\frac{1}{3}}\\\\=3\sqrt[3]{3}

konstantin123 [22]2 years ago
4 0

Answer:

The value remains under the radical is 3.

Step-by-step explanation:

Given : When 9 Superscript two-thirds is written in simplest radical form.

To find : Which value remains under the radical?

Solution :

The expression given 9 Superscript two-thirds is written as,

9^{\frac{2}{3}}

We re-write the expression as,  

9^{\frac{2}{3}}=(9^2)^{\frac{1}{3}}

9^{\frac{2}{3}}=\sqrt[3]{9^2}

9^{\frac{2}{3}}=\sqrt[3]{81}

9^{\frac{2}{3}}=\sqrt[3]{3\times 3\times 3\times 3}

9^{\frac{2}{3}}=3\sqrt[3]{3}

Therefore, the value remains under the radical is 3.

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