Question

1.​3¹×3²×3³×......×3⁸⁰
2.7¹×7²×7³×.....×7³⁴
3.4¹×4²×4³×......×4¹⁵
4.11¹×11²×11³×......×11²⁵
5.13¹×13²×13³×.....×13¹⁸
Va rog mult!Mulțumesc anticipat!Este urgent!!!!

Answer 1

1.

$3^1\times3^2\times3^3\times...\times3^{80}= 3^{1+2+3+...+80} \\1+2+3+...+80= \frac{80\times81}{2}= 40\times81=3240 \\3^1\times3^2\times3^3\times...\times3^{80}= 3^{3240}$

2.

$7^1\times7^2\times7^3\times...\times7^{34}=7^{1+2+3+...+34}\\1+2+3+...+34= \frac{34\times35}{2}= 17\times35=595\\7^1\times7^2\times7^3\times...\times7^{34}=7^{595}$

3.

$4^1\times4^2\times4^3\times...\times4^{15}= 4^{1+2+3+...+15}\\1+2+3+...+15= \frac{15\times16}{2}=15\times8= 120\\4^1\times4^2\times4^3\times...\times4^{15}=4^{120}$

4.

$11^1\times11^2\times11^3\times...\times11^{25}= 11^{1+2+3+...+25}\\1+2+3+...+25= \frac{25\times26}{2}= 25\times13= 325\\11^1\times11^2\times11^3\times...\times11^{25}= 11^{325}$

5.

$13^1\times13^2\times13^3\times...\times13^{18}= 13^{1+2+3+...+18}\\1+2+3+...+18= \frac{18\times19}{2}=9\times19= 171\\13^1\times13^2\times13^3\times...\times13^{18}= 13^{171}$