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Popular >

simplify \sqrt[3]{216^{a^4}}

Solution

simplify

Solution

6^{a^{4}}

Solution steps

Apply radical rule:

= (21 6^{a^{4}})^{\frac{1}{3}}

Apply exponent rule:

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

= 21 6^{a^{4} \frac{1}{3}}

Simplify

a^{4} \frac{1}{3} : \frac{a ^{4}}{3}

= 21 6^{\frac{a ^{4}}{3}}

Factor the number:

216 = 6^{3}

= (6^{3})^{\frac{a ^{4}}{3}}

Apply exponent rule:

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

(6^{3})^{\frac{a ^{4}}{3}} = 6^{3 \cdot \frac{a ^{4}}{3}} = 6^{a^{4}}

= 6^{a^{4}}

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Frequently Asked Questions (FAQ)

What is \sqrt[3]{216^{a^4}} ?
The solution to \sqrt[3]{216^{a^4}} is 6^{a^4}