Question

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Answer 1

Question :-

$\implies\sf \dfrac{9\times 10^9 \times 16 \times 10^{-6} \times 16 \times 10^{-6} }{(0.4)^2}$

Answer :-

$\implies\sf \dfrac{3^2 \times ( 5 \times 2)^9 \times 2^4 \times (5\times 2)^{-6} \times 2^4 \times (5\times 2)^{-6}}{0.16}$

$\implies\sf \dfrac{3^2 \times 5^9 \times 2^9 \times 2^4 \times 5^{-6} \times 2^{-6} \times 2^4 \times 5^{-6} \times 2^{-6}}{16 \times 10^{-2}}$

$\implies\sf \dfrac{3^2 \times ( 5^9 \times 5^{-6} \times 5^{-6}) \times (2^9 \times 2^4 \times 2^4 \times 2^{-6}\times 2^{-6} )}{2^4 \times (5\times 2)^{-2}}$

$\implies\sf \dfrac{3^2 \times 5^{9-6-6} \times 2^{9+4+4-6-6}}{2^4 \times 5^{-2} \times 2^{-2}}$

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

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

$\implies\sf 3^2 \times 5^{-3+2} \times 2^{5-2}$

$\implies\sf 3^2 \times 5^{-1} \times 2^3$

$\implies\sf 8 \times 9 \times 5^{-1}$

$\implies\sf \dfrac{72}{5}$

$\implies\boxed{\sf 14.4}$

Additional information :-

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

Answer 2

$\large\bf{Topic : Law~ of~ Exponents}$

$\large\sf\red{Refer~ the~ attachment}$