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7.Simplify :
(i)\(\frac{25\times t^{-4}}{5^{-3}\times10\times t^{-8}}(t\neq 0)\)

(ii)\(\frac{3^{-5}\times 10^{-5}\times 125}{5^{-7}\times 6^{-5}}\)


Answer :

(i)We have:\(\frac{25\times t^{-4}}{5^{-3}\times10\times t^{-8}}(t\neq 0)\)

\(=\frac{25\times 5^3}{10}\times t^{(-4+8)}=\frac{5\times 5^3}2\times t^4\)

\(=\frac{625}2t^4\)
(ii)We have:\(\frac{3^{-5}\times 10^{-5}\times 125}{5^{-7}\times 6^{-5}}\)

\(=\frac{5^{7}\times 6^{5}\times 125}{3^{5}\times 10^{5}}\)

\(=\frac{5^{7}\times (3\times 2)^{5}\times 5^3}{3^{5}\times (2\times5)^{5}}=\frac{5^{7}\times 3^{5}\times 2^5\times 5^3}{3^{5}\times 2^5\times5^{5}}=5^{7+3-5}=5^5\)