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4 votes
What is the simplest form of ^4√81x^8y^5?

User TAG
by
7.5k points

2 Answers

3 votes

Answer:


3x^2y\sqrt[4]{y}

Explanation:

We have been given the radical expression
\sqrt[4]{81x^8y^5}

We can rewrite the terms inside the radical as:


81=3^4\\x^8=(x^2)^4\\y^5=y^4\cdot y

Hence, the expression will become


\sqrt[4]{3^4\cdot(x^2)^4\cdot y^4\cdot y}

Apply the exponent rule:
\sqrt[n]{x^n}=x


=3\cdotx^2\cdot y\sqrt[4]{y}\\\\=3x^2y\sqrt[4]{y}

Hence, the simplified expression is
3x^2y\sqrt[4]{y}

User Thusithz
by
7.8k points
4 votes

\sqrt[4]{81 x^(8) y^(5)} = \sqrt[4]{(3 x^(2) y)^(4) y} = 3 x^(2) y \sqrt[4]{y}
User Betofarina
by
7.7k points

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