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Using laws of exponents, simplify and write the answer in exponential form:
$(i)$. $3^2\times3^4\times3^8$
$(ii)$. $6^{15}\div6^{10}$
$(iii)$. $a^3\times a^2$
$(iv)$. $7^x\times7^2$
$(v)$. $(5^2)^3\div5^3$
$(vi)$. $2^5\times5^5$
$(viii)$. $a^4\times b^4$
$(viii)$. $(3^4)^3$
$(ix)$. $(2^{20}\div2^{15})\times2^3$
$(x)$. $8^t\div8^2$
Given:
$(i)$. $3^2\times3^4\times3^8$
$(ii)$. $6^{15}\div6^{10}$
$(iii)$. $a^3\times a^2$
$(iv)$. $7^x\times7^2$
$(v)$. $(5^2)^3\div5^3$
$(vi)$. $2^5\times5^5$
$(vii)$. $a^4\times b^4$
$(viii)$. $(3^4)^3$
$(ix)$. $(2^{20}\div2^{15})\times2^3$
$(x)$. $8^t\div8^2$
To do: To simplify and write the answer in exponential form by using laws of exponents.
Solution:
$(i)$. $3^2\times3^4\times3^8$
$=[3^{2+4+8}]$ [As we know that $a^m\times a^n=a^{m+n}$]
$=3^{14}$
$(ii)$. $6^{15}\div6^{10}$
$=[6^{15-10}]$ $[a^m\div a^n=a^{m-n}]$
$=6^5$
$(iii)$. $a^3\times a^2$
$=[a^{3+2}]$ $[a^m\times a^n=a^{m+n}]$
$=a^5$
$(iv)$. $7^x\times7^2$
$=[7^{x+2}]$ $[a^m\times a^n=a^{m+n}]$
$(v)$. $(5^2)^3\div5^3$
$=5^{3\times2}\div5^3$ $[(a^m)^n=a^{mn}]$
$=5^6\div5^3$
$=5^{6-3}$ $[a^m\div a^n=a^{m-n}]$
$=5^3$
$(vi)$. $2^5\times5^5$
$=(2\times5)^5$ $a^m\times b^{m\ }=(a\times b)^m$
$=(10)^5$
$(vii)$. $a^4\times b^4$
$=(a\times b)^4$ $a^m\times b^{m}=(a\times b)^m$
$(viii)$. $(3^4)^3$
$=(3)^{4\times3}$ $[(a^m)^n=a^{mn}]$
$=3^{12}$
$(ix)$. $(2^5)\times2^3$
$=2^{5+3}$ $[a^m\times a^n=a^{m+n}]$
$=(2)^8$
$(x)$. $8^t\div8^2$
$=(8)^{t-2}$ $[a^m\div a^n=a^{m-n}]$
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