What is sqrt(5)\sqrt[3]{5^2}*\sqrt[4]{5^3} ?

The solution to sqrt(5)\sqrt[3]{5^2}*\sqrt[4]{5^3} is 5*5^{5/12}sqrt(5)

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simplify sqrt(5)\sqrt[3]{5^2}*\sqrt[4]{5^3}

simplify

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

Decimal Notation

21.86213 \dots

Solution steps

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

Apply exponent rule:

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

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

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

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

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

(3 x^{2}) \cdot (5 x y)

5^{- l o g_{5} (4)}

(3 x^{3} y^{2}) (2 x^{2} y^{4})

a \cdot t \cdot e^{- b \cdot t}

\frac{d}{d x} ((y^{2}) c e^{- 2 x})

What is sqrt(5)\sqrt[3]{5^2}*\sqrt[4]{5^3} ?
The solution to sqrt(5)\sqrt[3]{5^2}*\sqrt[4]{5^3} is 5*5^{5/12}sqrt(5)