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

The solution to \sqrt[6]{3^5}*\sqrt[6]{3^5} is 3\sqrt[3]{3^2}

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

simplify

Decimal Notation

6.24025 \dots

Solution steps

Apply radical rule:

= (3^{5})^{\frac{1}{6}} (3^{5})^{\frac{1}{6}}

Apply exponent rule:

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

(3^{5})^{\frac{1}{6}} (3^{5})^{\frac{1}{6}} = (3^{5})^{\frac{1}{6} + \frac{1}{6}}

= (3^{5})^{\frac{1}{6} + \frac{1}{6}}

\frac{1}{6} + \frac{1}{6} = \frac{1}{3}

= (3^{5})^{\frac{1}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 3^{5 \cdot \frac{1}{3}}

5 \cdot \frac{1}{3} = \frac{5}{3}

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

3^{\frac{5}{3}} = 3^{1 + \frac{2}{3}}

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

Apply exponent rule:

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

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

Refine

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

x + 1 (x + 1)

4 x^{2} - 16 x - 48

\frac{400}{6}

\frac{12}{30}

\frac{1}{\frac{2}{2}}

What is \sqrt[6]{3^5}*\sqrt[6]{3^5} ?
The solution to \sqrt[6]{3^5}*\sqrt[6]{3^5} is 3\sqrt[3]{3^2}