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

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

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

simplify

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

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

Decimal

5.69432 \dots

Solution steps

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

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

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

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

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

Apply exponent rule:

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

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

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

Join

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

a \cdot 3 a^{2}

2.9 \cdot 1 0^{- 4}

6 5^{5}

e^{2 t} e^{- 2 t}

x^{3} (x + 3)^{3} (x - 3)

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