What is \sqrt[3]{2}*\sqrt[4]{2}*\sqrt[12]{32} ?

The solution to \sqrt[3]{2}*\sqrt[4]{2}*\sqrt[12]{32} is 2

Popular >

simplify \sqrt[3]{2}\sqrt[4]{2}\sqrt[12]{32}

simplify

2

Solution steps

Apply radical rule:

2^{\frac{1}{3}} \cdot 2^{\frac{1}{4}} = 2^{\frac{7}{12}}

Factor integer

32 = 2^{5}

Apply exponent rule:

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

= 2^{\frac{7}{12}} \cdot 2^{5 \cdot \frac{1}{12}}

Refine

= 2^{\frac{7}{12}} \cdot 2^{\frac{5}{12}}

Apply exponent rule:

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

2^{\frac{7}{12}} \cdot 2^{\frac{5}{12}} = 2^{\frac{7}{12} + \frac{5}{12}}

= 2^{\frac{7}{12} + \frac{5}{12}}

Join

\frac{7}{12} + \frac{5}{12} : 1

= 2^{1}

Apply rule

a^{1} = a

= 2

\frac{2}{3} + \frac{1}{2} \cdot 3

lo g_{3} (4) - lo g_{3} (2)

\frac{13 !}{11 !}

- \frac{7}{9} \div \frac{9}{8}

\frac{9}{10} + \frac{8}{15} + \frac{13}{75}

What is \sqrt[3]{2}*\sqrt[4]{2}*\sqrt[12]{32} ?
The solution to \sqrt[3]{2}*\sqrt[4]{2}*\sqrt[12]{32} is 2