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Popular >

simplify \sqrt[6]{243}^{3/5}

Solution

simplify

Solution

3^{\frac{1}{2}}

+1

Decimal Notation

1.73205 \dots

Solution steps

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 24 3^{\frac{1}{6} \cdot \frac{3}{5}}

\frac{1}{6} \cdot \frac{3}{5} = \frac{1}{10}

= 24 3^{\frac{1}{10}}

Factor the number:

243 = 3^{5}

= (3^{5})^{\frac{1}{10}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

(3^{5})^{\frac{1}{10}} = 3^{5 \cdot \frac{1}{10}} = 3^{\frac{1}{2}}

= 3^{\frac{1}{2}}

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Frequently Asked Questions (FAQ)

What is \sqrt[6]{243}^{3/5} ?
The solution to \sqrt[6]{243}^{3/5} is 3^{1/2}