What is [(10^{-2/3})^6]^{-3/4} ?

The solution to [(10^{-2/3})^6]^{-3/4} is 1000

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simplify [(10^{-2/3})^6]^{-3/4}

simplify

[(1 0^{- \frac{2}{3}})^{6}]^{- \frac{3}{4}}

1000

Solution steps

[(1 0^{- \frac{2}{3}})^{6}]^{- \frac{3}{4}}

(1 0^{- \frac{2}{3}})^{6} : 1 0^{- 4}

= [1 0^{- 4}]^{- \frac{3}{4}}

Apply exponent rule:

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

= \frac{1}{( 1 0 ^{- 4} ) ^{\frac{3}{4}}}

(1 0^{- 4})^{\frac{3}{4}} : 1 0^{- 3}

= \frac{1}{1 0 ^{- 3}}

Apply exponent rule:

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

1 0^{- 3} = \frac{1}{1 0 ^{3}}

= \frac{1}{\frac{1}{1 0 ^{3}}}

Apply the fraction rule:

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

= \frac{1 0 ^{3}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 1 0^{3}

1 0^{3} = 1000

= 1000

5 e^{- 4 x}

(229.7)^{2}

4000 π \cdot 4.7 \cdot 1 0^{- 3}