What is sqrt(3)*\sqrt[3]{9}*\sqrt[4]{27} ?

The solution to sqrt(3)*\sqrt[3]{9}*\sqrt[4]{27} is 3*3^{5/12}sqrt(3)

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simplify sqrt(3)\sqrt[3]{9}\sqrt[4]{27}

simplify

3 \cdot 3^{\frac{5}{12}} 3

Decimal Notation

8.21263 \dots

Solution steps

Factor integer

9 = 3^{2}

Apply exponent rule:

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

Refine

Factor integer

27 = 3^{3}

Apply exponent rule:

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

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

Refine

= 3 \cdot 3^{\frac{2}{3}} \cdot 3^{\frac{3}{4}}

Apply exponent rule:

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

3^{\frac{2}{3}} \cdot 3^{\frac{3}{4}} = 3^{\frac{2}{3} + \frac{3}{4}}

= 3 \cdot 3^{\frac{2}{3} + \frac{3}{4}}

3^{\frac{2}{3} + \frac{3}{4}} = 3 \cdot 3^{\frac{5}{12}}

= 3 \cdot 3^{\frac{5}{12}} 3

\frac{x}{4} \leq \frac{9}{x}

\frac{2}{3} - \frac{2}{5}

2 m^{3} - m^{2} + 4 m - 2

∣ 5 - 5 x ∣ - 1 = 7

What is sqrt(3)*\sqrt[3]{9}*\sqrt[4]{27} ?
The solution to sqrt(3)*\sqrt[3]{9}*\sqrt[4]{27} is 3*3^{5/12}sqrt(3)