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Popular >

simplify \sqrt[3]{27^{a^3}}

Solution

simplify

Solution

3^{a^{3}}

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

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

Simplify

a^{3} \frac{1}{3} : \frac{a ^{3}}{3}

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

Factor the number:

27 = 3^{3}

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

Apply exponent rule:

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

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

= 3^{a^{3}}

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Frequently Asked Questions (FAQ)

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