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stich3 [128]
3 years ago
9

When 9^2/3 is written in simplest radical form, which value remains under the radical?

Mathematics
2 answers:
gayaneshka [121]3 years ago
8 0
First, change 9 into exponential form. 9 equals 3 squared. We change 9 into smaller number to find the simplest form of the radical later.
9^{\frac{2}{3}}
=(3^{2})^{\frac{2}{3}}
=3^{\frac{4}{3}}

Second, change into radical form
The denominator of fractional exponent is the root of the radical
3^{\frac{4}{3}}
= \sqrt[3]{ 3^{4}}

Third, simplify the exponential form under the radical using exponential property
= \sqrt[3]{ 3^{3+1}}
=  \sqrt[3]{3^{3} \times 3^{1}}
= \sqrt[3]{3^{3}}  \times \sqrt[3]{3}
= 3 \times \sqrt[3]{3}
= 3 \sqrt[3]{3}

In the simplest radical form, what remains under the radical is 3
PtichkaEL [24]3 years ago
4 0

Answer:3

Step-by-step explanation:

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