Question

Simplify the equation given in the picture

Answer 1

Question :-

Simplify :-

$\sf \dfrac{4\times 10^7 \times 6 \times 10^{-5}}{8 \times 10^4}$

Answer :-

$\implies\sf \dfrac{4\times 10^7 \times 6 \times 10^{-5}}{8 \times 10^4}$

$\implies\sf \dfrac{ 2 \times 2 \times 10^{7} \times 10^{-5} \times 2 \times 3}{2^3 \times 10^4}$

$\implies\sf \dfrac{2^2 \times 10^{7-5} \times 2 \times 3}{2^3 \times 10^4}$

$\implies\sf \dfrac{2^2 \times 2 \times 10^2 \times 3}{2^3 \times 10^4}$

$\implies\sf \dfrac{\cancel{2^3} \times 10^2 \times 3}{\cancel{2^3} \times 10^4}$

$\implies\sf \dfrac{10^2 \times 3}{10^4}$

$\implies\sf 10^{2-4} \times 3$

$\implies\sf 10^{-2} \times 3$

$\implies\sf \dfrac{3}{10^2}$

$\implies\sf \dfrac{3}{100}$

$\implies\boxed{\sf 0.03}$

Additional information :-

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$

Answer 2

Given : $\sf{\dfrac{4\times10^{7} \times 6 \times 10^{-5}}{8 \times 10^{4}}}$

To Simplify: $\sf{\dfrac{4 \times 10^{7} \times 6 \times 10^{-5}}{8 \times 10^{4}}}$

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⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Simplifying \: the \: Given \: Values \::}}$

⠀⠀⠀⠀⠀$:\implies \tt{\dfrac{4 \times 10^{7} \times 6 \times 10^{-5}}{8 \times 10^{4}}}$

⠀⠀⠀⠀⠀$:\implies \tt{\dfrac{2 \times 2 \times 10^{7} \times 2 \times 3 \times 10^{-5}}{2 \times 2 \times 2 \times 10^{4}}}$

⠀⠀⠀⠀⠀$:\implies \tt{\dfrac{2^{2} \times 10^{7} \times 2 \times 3 \times 10^{-5}}{2 ^{3} \times 10^{4}}}$

⠀⠀⠀⠀⠀$:\implies \tt{\dfrac{2^{3} \times 10^{7} \times 3 \times 10^{-5}}{2 ^{3} \times 10^{4}}}$

⠀⠀⠀⠀⠀$:\implies \tt{\dfrac{2^{3} \times 10^{7} \times 10^{-5}\times 3 }{2 ^{3} \times 10^{4}}}$

As We know that :

• $\star a^{x} \times a^{y} = a ^{x +y}$

⠀⠀⠀⠀⠀$:\implies \tt{\dfrac{2^{2} \times 10^{7- 5} \times 3 }{2 ^{3} \times 10^{4}}}$

⠀⠀⠀⠀⠀$:\implies \tt{\dfrac{\cancel {2^{3}} \times 10^{2} \times 3 }{\cancel {2 ^{3} }\times 10^{4}}}$

⠀⠀⠀⠀⠀$:\implies \tt{\dfrac{ 10^{2} \times 3 }{ 10^{4}}}$

As, We know that ,

• $\star \dfrac{a^{y}}{a^{x}}= a ^{y-x}$

⠀⠀⠀⠀⠀$:\implies \tt{ 10^{2-4} \times 3 }$

⠀⠀⠀⠀⠀$:\implies \tt{ 10^{-2} \times 3 }$

Or ,

⠀⠀⠀⠀⠀$:\implies \tt{ \dfrac{ 3}{10^{2}} }$

⠀⠀⠀⠀⠀$:\implies \tt{ \dfrac{ 3}{100} }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm { Answer \:= 0.03\: }}}}\:\bf{\bigstar}$

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