What is 5^{-8}0.2^{-8} ?

The solution to 5^{-8}0.2^{-8} is 1

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simplify 5^{-8}0.2^{-8}

simplify

5^{- 8} 0. 2^{- 8}

1

Solution steps

5^{- 8} \cdot 0. 2^{- 8}

5^{- 8} = \frac{1}{390625}

= \frac{1}{390625} \cdot 0. 2^{- 8}

Apply exponent rule:

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

0. 2^{- 8} = \frac{1}{0. 2 ^{8}}

= \frac{1}{390625} \cdot \frac{1}{0. 2 ^{8}}

0. 2^{8} = 0.00000256

= \frac{1}{390625} \cdot \frac{1}{0.00000256}

Divide the numbers:

\frac{1}{0.00000256} = 390625

= \frac{1}{390625} \cdot 390625

Convert element to fraction:

390625 = \frac{390625}{1}

= \frac{1}{390625} \cdot \frac{390625}{1}

Cross-cancel common factor:

390625

= 1

e^{- 0.8} (0.8)^{2}

e^{- (- 1)^{3}}

\frac{c}{x}

x^{- \frac{1}{2}} ln (x)

25 e^{- 0.5 (8)}