What is \sqrt[600]{3000^{400}} ?

The solution to \sqrt[600]{3000^{400}} is 100*3^{2/3}

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simplify \sqrt[600]{3000^{400}}

simplify

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

Decimal Notation

208.00838 \dots

Solution steps

Apply radical rule:

= (300 0^{400})^{\frac{1}{600}}

Apply exponent rule:

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

= 300 0^{400 \cdot \frac{1}{600}}

400 \cdot \frac{1}{600} = \frac{2}{3}

= 300 0^{\frac{2}{3}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 1 0^{2} \cdot 3^{\frac{2}{3}}

1 0^{2} = 100

= 100 \cdot 3^{\frac{2}{3}}

e^{- 16.8}

e^{- 16.7}

(e^{- x})^{n}

2.43 \cdot 1 0^{- 9}

- 20 e^{- 2 (0.5)}

What is \sqrt[600]{3000^{400}} ?
The solution to \sqrt[600]{3000^{400}} is 100*3^{2/3}