Q4. Evaluate

    (i) \frac{8^{-1}\times 5^{3}}{2^{-4}}

Answers (1)

The detailed explanation for the above written question is as follows

\frac{8^{-1}\times 5^{3}}{2^{-4}}

after rewriting the above equation we get,

\frac{2^{-3}\times 5^{3}}{2^{-4}}       =2^{-3-(-4)}\times 5^{3}  ...........as we know that  \frac{a^{m}}{a^{n}}= a^{m-n}

                         \\=2^{1}\times 5^{3}\\ = 2\times 125 = 250

  

An alternate method,

= \frac{5^{3}}{2^{-4}\times 2^{3}}

here you can use first a^{-m}= \frac{1}{a^{m}}  and after that use a^{m}\times a^{n}= a^{m+n}

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