How to simplify ${(7.87 \times 10^{- 1})}^{- 6}$ $(7.87 times 10^-1)^-6$ in scientific notation?

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How to simplify ${(7.87 \times 10^{- 1})}^{- 6}$ $(7.87 times 10^-1)^-6$ in scientific notation?

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Answer 1 · 2016-06-08T09:06:41

${(7.87 \times 10^{- 1})}^{- 6} = 4.2087$ $(7.87xx10^(-1))^(-6)=4.2087$

Explanation:

As $a^{- m} = \frac{1}{a^{m}}$ $a^(-m)=1/a^m$ , ${(a b)}^{n} = a^{n} \times b^{n}$ $(ab)^n=a^nxxb^n$ , ${(a^{m})}^{n} = a^{m \times n}$ $(a^m)^n=a^(mxxn)$ and ${(\frac{a}{b})}^{n} = \frac{a^{n}}{b^{n}}$ $(a/b)^n=a^n/b^n$

${(7.87 \times 10^{- 1})}^{- 6}$ $(7.87xx10^(-1))^(-6)$

= ${7.87}^{- 6} \times {(10^{- 1})}^{- 6}$ $7.87^(-6)xx(10^(-1))^(-6)$

= $\frac{1}{{7.87}^{6}} \times 10^{(- 1) \times (- 6)}$ $1/7.87^6xx10^((-1)xx(-6))$

= $\frac{1}{237601.07} \times 10^{6}$ $1/237601.07xx10^6$

= $\frac{1000000}{237601.07}$ $1000000/237601.07$

= $4.2087$ $4.2087$

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How to simplify ${(7.87 \times 10^{- 1})}^{- 6}$ $(7.87 times 10^-1)^-6$ in scientific notation?

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Explanation:

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