What is (((2^3)^{-4})^3)^{-1} ?

The solution to (((2^3)^{-4})^3)^{-1} is 2^{36}

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simplify (((2^3)^{-4})^3)^{-1}

simplify

(((2^{3})^{- 4})^{3})^{- 1}

2^{36}

Decimal Notation

68719476736

Solution steps

(((2^{3})^{- 4})^{3})^{- 1}

(2^{3})^{- 4} : 2^{- 12}

= ((2^{- 12})^{3})^{- 1}

Apply exponent rule:

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

= \frac{1}{( 2 ^{- 12} ) ^{3}}

(2^{- 12})^{3} : 2^{- 36}

= \frac{1}{2 ^{- 36}}

Apply exponent rule:

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

2^{- 36} = \frac{1}{2 ^{36}}

= \frac{1}{\frac{1}{2 ^{36}}}

Apply the fraction rule:

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

= \frac{2 ^{36}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 2^{36}

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