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Popular >

simplify \sqrt[5]{(243)^3}

Solution

simplify

Solution

27

Solution steps

Apply radical rule:

= ((243)^{3})^{\frac{1}{5}}

Apply exponent rule:

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

= (243)^{3 \cdot \frac{1}{5}}

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

= (243)^{\frac{3}{5}}

Factor the number:

243 = 3^{5}

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

Apply exponent rule:

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

(3^{5})^{\frac{3}{5}} = 3^{5 \cdot \frac{3}{5}} = 3^{3}

= 3^{3}

Refine

= 27

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Frequently Asked Questions (FAQ)

What is \sqrt[5]{(243)^3} ?
The solution to \sqrt[5]{(243)^3} is 27