Question

Calculați valoarea expresiei: $\frac{12^{5}*8^{-3}}{3^{5}}$

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Answer 1

Răspuns:

$\displaystyle \frac{12^{5} * 8^{-3}}{3^{5} } = \\\\ \displaystyle \frac{4^{5} * 3^{5} * 8^{-3} }{ 3^{5} } = \\\\ \displaystyle 4^{5} * 8^{-3} = \\\\ \displaystyle (2^{2}) ^{5} *( 2^{3})^{-3} = \\\\ \displaystyle 2^{10} * 2^{-9} = \\\\ \displaystyle 2^{10 + (-9)} = \\\\ \displaystyle 2^{1} = \\\\\boxed {2}$

Answer 2

$\it\dfrac{12^5\cdot8^{-3}}{3^5}=\dfrac{(3\cdot4)^5\cdot(2^3)^{-3}}{3^5}=\dfrac{3^5\cdot(2^2)^5\cdot2^{-9}}{3^5}=2^{10}\cdot2^{-9}=2^{10-9}=2$