Question

 \frac{2^{6}}{( 2^{-5} *8)^{-2}};
\frac{9^{-4}*4^{-4}}{2^{-9}*3{-9}};
\frac{5^{5}*25{-2}}{5{-3}*125.} [/tex]

Answer 1

$\frac{2^{6}}{( 2^{-5} *8)^{-2}}$

$\frac{9^{-4}\cdot4^{-4}}{2^{-9}\cdot3^{-9}}$

$\frac{5^{5}\cdot25^{-2}}{5^{-3}\cdot125.}$

La primul, scriem totul ca puteri a lui 2 si folosim proprietatile calculului cu puteri:

$\dfrac{2^6}{(2^{-5}\cdot 2^3)^{-2}}=\dfrac{2^6}{2^{10}\cdot 2^{-6}}=\dfrac{2^6}{2^4}=2^2=4.$

La a doua facem puteri a lui 2 si 3 si apoi din nou folosim proprietati ale puterilor:

$\dfrac{(3^2)^{-4}\cdot (2^2)^{-4}}{2^{-9}\cdot 3^{-9}}=\dfrac{3^{-8}\cdot 2^{-8}}{2^{-9}\cdot 3^{-9}}=\dfrac{1}{2^{-1}\cdot 3^{-1}}=2\cdot 3=6.$

La ultima e aceeasi idee:

$\dfrac{5^5\cdot 5^{-4}}{5^{-3}\cdot 5^3}=\dfrac{5^1}{5^0}=5.$