Question

Folosind regula de înmulțire a puterilor cu aceeași bază, scrie fiecare din următoarele produse cu cel mai mic număr de factori

Answer 1

$a)3^{11}\cdot5^{8}\cdot3^{14}\cdot5^{17}=3^{11+14}\cdot5^{17+8}=3^{25}\cdot5^{25}=(3\cdot5)^{25}=15^{25}$

$b)2^{2}\cdot3^{3}\cdot2^{4}\cdot3^{5}=2^{2+4}\cdot3^{3+5}=2^{6}\cdot3^{8}$

$c)(3^{4}\cdot7^{2})\cdot3\cdot(3^{4}\cdot7^{2})^{4}=(3^{4\cdot7^{2})}^{4+1}\cdot3=(3^{4}\cdot7^{2})^{5}\cdot3=3^{4\cdot5}\cdot7^{2\cdot5}\cdot3=3^{20}\cdot7^{10}\cdot3=3^{21}\cdot7^{10}$

$d)(5^{2}\cdot7)^{2}\cdot(5^{7}\cdot7^{4})=(5^{2\cdot3}\cdot7^{2})\cdot(5^{7}\cdot7^{4})=5^{6-7}\cdot7^{2-4}=\frac{1}{5^{3}\cdot7^{2}}$

$e)(3\cdot x)^{11}\cdot4\cdot x=3^{11}\cdot x^{11}\cdot4\cdot x=3^{11}\cdot4\cdotx^{12}$

$f)(2\cdot x\cdot y^{2})^{3}\cdot x\cdot y=2\cdot x^{3}\cdot y^{6}\cdot y\cdot x=2\cdot x^{4}\cdot y^{7}=$

$g)5^{3}\cdot x^{6}\cdot4\cdotx=5^{3}\cdot4\cdot x^{7}$

$h) (x^{6}\cdot y^{2}\cdot z^{8})^{3}\cdot(x^{9}\cdot y^{3}\cdot z^{12})^{2}=(x^{6\cdot3}\cdot y^{2\cdot3}\cdot z^{8\cdot3})\cdot(x^{9\cdot2}\cdot y^{2\cdot3}\cdot z^{12\cdot2})=x^{12+12}\cdoty^{6+6}\cdot z^{24+24}=x^{36}\cdot y^{12}\cdot z^{48}$