# Simplify:$(i)$. $\frac{(2^5)^2\times7^3}{8^3\times7}$$(ii). \frac{25\times5^2\times t^8}{10^3\times t^4}$$(iii)$. $\frac{3^5\times10^5\times25}{5^7\times6^5}$

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Given:

$(i)$. $\frac{(2^5)^2\times7^3}{8^3\times7}$

$(ii)$. $\frac{25\times5^2\times t^8}{10^3\times t^4}$

$(iii)$. $\frac{3^5\times10^5\times25}{5^7\times6^5}$

To do: To simplify each of the above expressions.

Solution:

$(i)$. $\frac{(2^5)^2\times7^3}{8^3\times7}$

$=\frac{(2^{5})^2\times7^3}{(2^3)^3\times7}$

$=\frac{2^{10}\times7^3}{2^9\times7}$

$=(2^{10-9})\times(7^{3-1})$

$=2^1\times7^2$

$=2\times49$

$=98$

$(ii)$. $\frac{25\times5^2\times t^8}{10^3\times t^4}$

$=\frac{5^2\times5^2\times t^8}{(5\times2)^3\times t^4}$

$=\frac{5^{2+2}\times t^{8-4}}{5^3\times2^3}$

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

$=\frac{5^1\times t^4}{8}$

$=\frac{5t^4}{8}$

$(iii)$. $\frac{3^5\times10^5\times25}{5^7\times6^5}$

$=\frac{3^5(2\times5)^5\times5^2}{5^7\times(2\times3)^5}$

$=\frac{(3^5\times2^5\times5^{5+2})}{5^7\times2^5\times3^5}$

$=\frac{3^5\times2^5\times5^7}{5^7\times2^5\times3^5}$

$=2^0\times3^0\times5^0$

$=1\times1\times1$

$=1$
Updated on 10-Oct-2022 13:38:51