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Popular >

simplify \sqrt[3]{27^m}

Solution

simplify

Solution

3^{m}

Solution steps

Apply radical rule:

= (2 7^{m})^{\frac{1}{3}}

Apply exponent rule:

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

= 2 7^{m \frac{1}{3}}

Simplify

m \frac{1}{3} : \frac{m}{3}

= 2 7^{\frac{m}{3}}

Factor the number:

27 = 3^{3}

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

Apply exponent rule:

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

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

= 3^{m}

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Frequently Asked Questions (FAQ)

What is \sqrt[3]{27^m} ?
The solution to \sqrt[3]{27^m} is 3^m