What is \sqrt[3]{\sqrt[4]{16}} ?

The solution to \sqrt[3]{\sqrt[4]{16}} is cube root of 2

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simplify \sqrt[3]{\sqrt[4]{16}}

simplify

Decimal Notation

1.25992 \dots

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

= 1 6^{\frac{1}{4} \cdot \frac{1}{3}}

\frac{1}{4} \cdot \frac{1}{3} = \frac{1}{12}

= 1 6^{\frac{1}{12}}

Factor the number:

16 = 2^{4}

Apply exponent rule:

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

e^{(- \frac{t}{2})}

(1 - 3 x)^{- 3}

(3.4 \times 1 0^{5}) (1.2 \times 1 0^{- 3})

\frac{4 ^{n}}{3 ^{n}}

What is \sqrt[3]{\sqrt[4]{16}} ?
The solution to \sqrt[3]{\sqrt[4]{16}} is cube root of 2