What is (sqrt(2)^{-(3pi)/4})^7 ?

The solution to (sqrt(2)^{-(3pi)/4})^7 is 1/(2^{\frac{21pi){8}}}

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simplify (sqrt(2)^{-(3pi)/4})^7

simplify

(2^{- \frac{3 π}{4}})^{7}

\frac{1}{2 ^{\frac{21 π}{8}}}

Solution steps

((2)^{- \frac{3 π}{4}})^{7}

(2)^{- \frac{3 π}{4}} : 2^{- \frac{3 π}{8}}

= (2^{- \frac{3 π}{8}})^{7}

Apply exponent rule:

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

= 2^{(- \frac{3 π}{8}) \cdot 7}

(- \frac{3 π}{8}) \cdot 7 = - \frac{21 π}{8}

= 2^{- \frac{21 π}{8}}

Apply exponent rule:

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

= \frac{1}{2 ^{\frac{21 π}{8}}}

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5 (53)

What is (sqrt(2)^{-(3pi)/4})^7 ?
The solution to (sqrt(2)^{-(3pi)/4})^7 is 1/(2^{\frac{21pi){8}}}