Question

Stiind ca x, y, z si t sunt nr naturale nenule, calculeaza: a) (143 la puterea x : 11 la puterea x+91 la puterea x : 7 la puterea x +169 la puterea x : 13 la puterea x):13 la puterea x​

Answer 1

 

$\displaystyle\bf\\\big(143^x:11^x+91^x:7^x+169^x:13^x\big):13^x=\\\\=\frac{143^x:11^x+91^x:7^x+169^x:13^x}{13^x}=\\\\\\=\frac{\dfrac{143^x}{11^x}+\dfrac{91^x}{7^x}+\dfrac{169^x}{13^x}}{13^x}=\\\\\\=\frac{\dfrac{(13\cdot11)^x}{11^x}+\dfrac{(13\cdot7)^x}{7^x}+\dfrac{(13\cdot13)^x}{13^x}}{13^x}=\\\\\\=\frac{\dfrac{13^x\cdot11^x}{11^x}+\dfrac{13^x\cdot7^x}{7^x}+\dfrac{13^x\cdot13^x}{13^x}}{13^x}=\\\\\\=\frac{13^x+13^x+13^x}{13^x}=\\\\\\=\frac{3\cdot13^x}{13^x}=\boxed{\bf3}$