What is \sqrt[4]{3^3}*\sqrt[6]{3^5} ?

The solution to \sqrt[4]{3^3}*\sqrt[6]{3^5} is 3*3^{7/12}

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simplify \sqrt[4]{3^3}*\sqrt[6]{3^5}

simplify

4 3^{3} \cdot 6 3^{5}

3 \cdot 3^{\frac{7}{12}}

Decimal

5.69432 \dots

Solution steps

4 3^{3} 6 3^{5}

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

= 3^{\frac{3}{4}} 6 3^{5}

6 3^{5} : 3^{\frac{5}{6}}

= 3^{\frac{3}{4}} \cdot 3^{\frac{5}{6}}

Apply exponent rule:

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

3^{\frac{3}{4}} \cdot 3^{\frac{5}{6}} = 3^{\frac{3}{4} + \frac{5}{6}}

= 3^{\frac{3}{4} + \frac{5}{6}}

Join

\frac{3}{4} + \frac{5}{6} : \frac{19}{12}

= 3^{\frac{19}{12}}

3^{\frac{19}{12}} = 3^{1 + \frac{7}{12}}

= 3^{1 + \frac{7}{12}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

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

Refine

= 3 \cdot 3^{\frac{7}{12}}

x \times a

(3 x^{2}) (7 x^{3})

\frac{x ^{2} - 1}{x ^{2} + 2}

\frac{4 3}{4 5}

e^{(- 2 l n (x^{2} + 1))}

What is \sqrt[4]{3^3}*\sqrt[6]{3^5} ?
The solution to \sqrt[4]{3^3}*\sqrt[6]{3^5} is 3*3^{7/12}