What is (sqrt((\sqrt{3))^3})^4 ?

The solution to (sqrt((\sqrt{3))^3})^4 is 27

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simplify (sqrt((\sqrt{3))^3})^4

simplify

((3)^{3})^{4}

27

Solution steps

((3)^{3})^{4}

Rewrite

4

2 \cdot 2

= ((3)^{3})^{2 \cdot 2}

Apply exponent rule:

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

((3)^{3})^{2 \cdot 2} = ((3)^{3})^{2}^{2}

= ((3)^{3})^{2}^{2}

Apply exponent rule:

((3)^{3})^{2} = (3)^{3}

= ((3)^{3})^{2}

Apply exponent rule:

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

= (3)^{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= (3)^{6}

Apply radical rule:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{6}

Apply exponent rule:

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

= 3^{\frac{1}{2} \cdot 6}

\frac{1}{2} \cdot 6 = 3

= 3^{3}

3^{3} = 27

= 27

85^{2}

800 e^{- 0.0244 (10)}

e^{- 2 t} u (t)