What is ((2^{-2})^3)^{-5} ?

The solution to ((2^{-2})^3)^{-5} is 2^{30}

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simplify ((2^{-2})^3)^{-5}

simplify

((2^{- 2})^{3})^{- 5}

2^{30}

Solution steps

((2^{- 2})^{3})^{- 5}

(2^{- 2})^{3} : 2^{- 6}

= (2^{- 6})^{- 5}

Apply exponent rule:

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

= \frac{1}{( 2 ^{- 6} ) ^{5}}

(2^{- 6})^{5} : 2^{- 30}

= \frac{1}{2 ^{- 30}}

Apply exponent rule:

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

2^{- 30} = \frac{1}{2 ^{30}}

= \frac{1}{\frac{1}{2 ^{30}}}

Apply the fraction rule:

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

= \frac{2 ^{30}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 2^{30}

e^{- 1} \cdot 1.125

4.06 \cdot 1 0^{- 3}

6 x^{- 0.75} (1 + x)

12 \cdot 2.7 1^{- 2}

1.421 e^{- 9}