Question

Plz..... Solve this questions for me...

Answer 1

`6.\\\text{We know}\ 9=3^2.\ \text{Therefore}\\\\9^2=(3^2)^2\\\\\text{use}\ (a^n)^m=a^(nm)\\\\9^2=(3^2)^2=3^(2\cdot2)=3^4\\\\\boxed{3^4=9^2}\\=================`

`7.\\METHOD\ 1:\\\\√(7^4)=\sqrt{7^(2\cdot2)}\\\\\text{use}\ (a^n)^m=a^(nm)\\\\=√((7^2)^2)\\\\\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=\boxed{7^2}\\\\METHOD\ 2:\\\\\text{use}\ a^(m)/(n)=\sqrt[n]{a^m}\\\\√(7^4)=7^(4)/(2)=\boxed{7^2}\\=================`

`8.\\5^a*5^b=5^(11)\\\\a)\\\text{use}\ a^n* a^m=a^(n+m)\\\\5^a*5^b=5^(a+b)\\\\5^(a+b)=5^(11)\Rightarrow a+b=11\\\\11\ \text{is odd. The sum of even and odd is odd. Therefore}\ a\ \text{and}\ b\ \text{can't be even.}\\--------------------\\\\b)\\5\ \text{solutions}\\\\11=5+6\\11=4+7\\11=3+8\\11=2+9\\11=1+10`