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

The solution to \sqrt[5]{6^3}*\sqrt[6]{6^5} is 6*6^{13/30}

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

simplify

6 \cdot 6^{\frac{13}{30}}

Solution steps

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

Apply exponent rule:

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

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

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

Join

\frac{3}{5} + \frac{5}{6} : \frac{43}{30}

= 6^{\frac{43}{30}}

6^{\frac{43}{30}} = 6^{1 + \frac{13}{30}}

= 6^{1 + \frac{13}{30}}

Apply exponent rule:

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

= 6^{1} \cdot 6^{\frac{13}{30}}

Refine

= 6 \cdot 6^{\frac{13}{30}}

2 - 3 \cdot 2 + 3

(3 y)^{2}

14 y (15 x^{4} y)

What is \sqrt[5]{6^3}*\sqrt[6]{6^5} ?
The solution to \sqrt[5]{6^3}*\sqrt[6]{6^5} is 6*6^{13/30}