What is (-(64/27)(2-8/7))^{-0.5} ?

The solution to (-(64/27)(2-8/7))^{-0.5} is -0.70156…i

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simplify (-(64/27)(2-8/7))^{-0.5}

simplify

(- (\frac{64}{27}) (2 - \frac{8}{7}))^{- 0.5}

- 0.70156 \dots i

Solution steps

(- (\frac{64}{27}) (2 - \frac{8}{7}))^{- 0.5}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{- \frac{64}{27} ( 2 - \frac{8}{7} )}

- \frac{64}{27} (2 - \frac{8}{7}) = i \frac{8 2}{3 7}

= \frac{1}{i \frac{8 2}{3 7}}

Multiply

i \frac{8 2}{3 7} : \frac{8 2 i}{3 7}

= \frac{1}{\frac{8 2 i}{3 7}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{3 7}{8 2 i}

Convert element to a decimal form

2 = 1.41421 \dots

= \frac{3 7}{8 \cdot 1.41421 \dots i}

Convert element to a decimal form

7 = 2.64575 \dots

= \frac{3 \cdot 2.64575 \dots}{8 \cdot 1.41421 \dots i}

Multiply the numbers:

8 \cdot 1.41421 \dots = 11.31370 \dots

= \frac{3 \cdot 2.64575 \dots}{11.31370 \dots i}

Multiply the numbers:

3 \cdot 2.64575 \dots = 7.93725 \dots

= \frac{7.93725 \dots}{11.31370 \dots i}

Divide the numbers:

\frac{7.93725 \dots}{11.31370 \dots} = 0.70156 \dots

= \frac{0.70156 \dots}{i}

Rationalize

\frac{0.70156 \dots}{i} : - 0.70156 \dots i

= - 0.70156 \dots i

(1.1176) (8.3 \cdot 1 0^{- 5}) (- 25)

(26) 6

e^{- \frac{y}{θ} (θ - 1)}

e^{x} e^{w}

\frac{1}{2} e^{- \frac{x}{2}} \cdot \frac{1}{3} e^{\frac{t - x}{3}}

What is (-(64/27)(2-8/7))^{-0.5} ?
The solution to (-(64/27)(2-8/7))^{-0.5} is -0.70156…i