What is 1/2 \sqrt[3]{128} ?

The solution to 1/2 \sqrt[3]{128} is 2\sqrt[3]{2}

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simplify 1/2 \sqrt[3]{128}

simplify

\frac{1}{2} 3128

232

Decimal

2.51984 \dots

Solution steps

\frac{1}{2} 3128

Prime factorization of

128 : 2^{7}

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

2^{7} = 2^{6} \cdot 2

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

Apply radical rule:

n ab = n a n b, a \geq 0, b \geq 0

3 2^{6} \cdot 2 = 3 2^{6} 32

= \frac{1}{2} 3 2^{6} 32

3 2^{6} = 4

= \frac{1}{2} \cdot 432

\frac{1}{2} \cdot 432 = 232

= 232

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