What is \sqrt[3]{sqrt(4*2^5)} ?

The solution to \sqrt[3]{sqrt(4*2^5)} is 2\sqrt[6]{2}

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simplify \sqrt[3]{sqrt(4*2^5)}

simplify

Decimal Notation

2.24492 \dots

Solution steps

4 \cdot 2^{5} = 82

Apply radical rule:

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

2 = 2^{\frac{1}{2}}

Apply radical rule:

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(2^{\frac{1}{2}})^{\frac{1}{3}} = 2^{\frac{1}{2} \cdot \frac{1}{3}}

= 2 \cdot 2^{\frac{1}{2} \cdot \frac{1}{3}}

\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}

= 2 \cdot 2^{\frac{1}{6}}

Apply exponent rule:

3.9 \cdot 1 0^{- 7}

2100 e^{- \frac{17}{20}}

\frac{e ^{12 x}}{e ^{\frac{4}{3} x}}

(2)^{27}

x x + h

What is \sqrt[3]{sqrt(4*2^5)} ?
The solution to \sqrt[3]{sqrt(4*2^5)} is 2\sqrt[6]{2}