What is [(4^{-2})^2]^{-5} ?

The solution to [(4^{-2})^2]^{-5} is 4^{20}

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simplify [(4^{-2})^2]^{-5}

simplify

[(4^{- 2})^{2}]^{- 5}

4^{20}

Solution steps

[(4^{- 2})^{2}]^{- 5}

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

= [4^{- 4}]^{- 5}

Apply exponent rule:

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

= \frac{1}{( 4 ^{- 4} ) ^{5}}

(4^{- 4})^{5} : 4^{- 20}

= \frac{1}{4 ^{- 20}}

Apply exponent rule:

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

4^{- 20} = \frac{1}{4 ^{20}}

= \frac{1}{\frac{1}{4 ^{20}}}

Apply the fraction rule:

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

= \frac{4 ^{20}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 4^{20}

e^{- 2 x} (8 x^{3} - 4 x^{4})

8 x^{6} (4 x^{3})

(1.58 \cdot 1 0^{- 5}) \cdot 0.25

- 2 \cdot 2 + x

7.81 \cdot 1 0^{- 2}