Question

(0,03)⁴ * (2^8 - 4²)³ =

Answer 1

$(0.03)^4*(2^8-4^2)^3=\\\\ =(\frac{3}{100})^4*[2^{2*4}-4^2]^3=\\\\ =\frac{3^4}{100^4}*[(2^2)^4-4^2]^3=\\\\ =\frac{3^4}{25^4*4^4}*[4^4-4^2]^3=\\\\ =\frac{3^4}{25^4*4^4}*[4^2*(4^2-1)]^3=\\\\ =\frac{3^4}{25^4*4^4}*4^6*15^3=\\\\ =\frac{3^4*4^6*5^3*3^3}{5^8*4^4}=\\\\ =\frac{3^7*4^2}{5^5}$

Answer 2

$(0.03)^4*(2^8-4^2)^3=( \frac{3}{100} )^4*(16^2-16)^3= (\frac{3}{100} )^4*(16*15)^3=\\ (\frac{3}{100}) ^4*16^3*15^3= \frac{3^4}{100^4}*2^{12} *3^3*5^3= \frac{3^7*2^{12}*5^3}{100^4} =\\ \frac{3^7*2^{12}*5^3}{5^8*2^8} = \frac{3^7*2^4}{5^5}$
Ответ: $\frac{3^7*2^4}{5^5}$