What is (\sqrt[3]{sqrt(\sqrt{-5/3)}})^{24} ?

The solution to (\sqrt[3]{sqrt(\sqrt{-5/3)}})^{24} is 25/9

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simplify (\sqrt[3]{sqrt(\sqrt{-5/3)}})^{24}

simplify

\frac{25}{9}

Decimal Notation

2.77777 \dots

Solution steps

Rewrite

24

3 \cdot 8

Apply exponent rule:

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

Apply exponent rule:

= - \frac{5}{3}^{8}

- \frac{5}{3} = i \frac{5}{3}

= i \frac{5}{3}^{8}

Apply radical rule:

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

= (i \frac{5}{3})^{\frac{1}{2}}^{8}

Apply exponent rule:

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

= (i \frac{5}{3})^{\frac{1}{2} \cdot 8}

\frac{1}{2} \cdot 8 = 4

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

Apply exponent rule:

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

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

(\frac{5}{3})^{4} : (\frac{5}{3})^{2}

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

Apply exponent rule:

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

5^{2} i^{4} = 25

= \frac{25}{3 ^{2}}

3^{2} = 9

= \frac{25}{9}

a e^{- x}

P^{1} (4, 5) P^{2} (7, 4) P^{3} (2, - 4)

(\frac{10}{3})^{3} x 0. 3^{- 1}

x^{- 6}

\frac{- 12}{- 2}

What is (\sqrt[3]{sqrt(\sqrt{-5/3)}})^{24} ?
The solution to (\sqrt[3]{sqrt(\sqrt{-5/3)}})^{24} is 25/9