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100 POINTS!! Express in radical form.

100 POINTS!! Express in radical form.-example-1

2 Answers

4 votes

Answer:


\large\boxed{27\sqrt[4]{x^3}}

Explanation:


\sqrt[n]{a^m}=a^(m)/(n)\\\\(ab)^n=a^nb^n\\\\\sqrt[n]{a^n}=a\\\\\sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\--------------------\\\\(81x)^(3)/(4)=\sqrt[4]{(81x)^3}=\sqrt[4]{81^3x^3}=\sqrt[4]{81^3}\cdot\sqrt[4]{x^3}=\sqrt[4]{(3^4)^3}\cdot\sqrt[4]{x^3}\\\\=\sqrt[4]{(3^3)^4}\cdot\sqrt[4]{x^3}=3^3\sqrt[4]{x^3}=27\sqrt[4]{x^3}

User Inoyatulloh
by
8.1k points
2 votes

Answer:

27 4th root (x^3)

Explanation:

(81x) ^ 3/4

We know (ab) ^c = a^c b^c

81 ^ (3/4) * x^3/4

We can rewrite 81 as 3^4

(3^4)^(3/4) * x^3/4

We know that a^b^c = a^ (b*c)

3^(4*3/4) * x^3/4

3^(3) * x^3/4

27 * x^3/4

27 4th root (x^3)

User Zelta
by
8.0k points

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