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

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

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

simplify

4^{\frac{4}{5}} x^{\frac{12}{5}}

Solution steps

Apply radical rule:

= ((2^{2} x^{3})^{\frac{1}{5}})^{4}

Apply exponent rule:

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

= (2^{2} x^{3})^{\frac{1}{5} \cdot 4}

\frac{1}{5} \cdot 4 = \frac{4}{5}

= (2^{2} x^{3})^{\frac{4}{5}}

2^{2} = 4

= (4 x^{3})^{\frac{4}{5}}

Apply exponent rule:

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

= 4^{\frac{4}{5}} (x^{3})^{\frac{4}{5}}

(x^{3})^{\frac{4}{5}} : x^{\frac{12}{5}}

= 4^{\frac{4}{5}} x^{\frac{12}{5}}

1.6 \cdot 1 0^{- 19} \cdot 6

1.745 \cdot 1 0^{- 2} \cdot 60

7.81 \cdot 1 0^{- 3}

e^{- x} (- 5 e^{- 5 x})

(2 x^{8}) (4 x^{4})

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