110. Stepenovanje | Balkan Tutor

Uprostiti izraz:

\bigg(\frac {2^x+2^{-x}} 2 \bigg)^2- \bigg(\frac {2^x-2^{-x}} 2 \bigg)^2

Primeniti definiciju za razliku kvadrata:

\bigg(\frac {2^x+2^{-x}} 2 - \frac {2^x-2^{-x}} 2 \bigg)\bigg(\frac {2^x+2^{-x}} 2 + \frac {2^x-2^{-x}} 2 \bigg) = \bigg(\frac {2^x+2^{-x}-2^x+2^{-x}} 2 \bigg)\bigg(\frac {2^x+2^{-x}+2^x-2^{-x}} 2 \bigg)

Srediti razlomak:

\bigg(\frac {\cancel{2^x}+2^{-x}-\cancel{2^x}+2^{-x}} 2 \bigg)\bigg(\frac {2^x+\cancel{2^{-x}}+2^x-\cancel{2^{-x}}} 2 \bigg) = \frac { 2*2^{-x}} 2 \frac {2*2^x} 2

Srediti razlomak:

\frac {\cancel{2}*2^{-x}} {\cancel{2}} \frac {\cancel{2}*2^x} {\cancel{2}} = 2^{-x}*2^x

Primeniti definiciju stepenovanja: $a^{-m}={\frac 1 {a^m}} ,$ $a{=}\mathllap{/\,} 0$

\frac {2^x} {2^x}

Primeniti osnovnu osobinu operacija sa stepenima: $\frac {a^m} {a^n}=a^{m-n}$ i definiciju stepenovanja: $a^0=1 ,$ $a{=}\mathllap{/\,} 0 :$

2^{x-x}=2^0=1

110.Stepenovanje