Question

Which expressions are equivalent to the one below? Check all that apply. 36^x/6^x

Answer 1

`\large(36^x)/(6^x)=\left((36)/(6)\right)^x=(6^(2x))/(6^x)=6^x`

Explanation:

`(36^x)/(6^x)\qquad\text{use}\ \left((a)/(b)\right)^n=(a^n)/(b^n)\\\\=\left((36)/(6)\right)^x=6^x\\\\36=6\cdot6=6^2\\\\(36^x)/(6^x)=((6^2)^x)/(6^x)\qquad\text{use}\ (a^n)^m=a^(nm)\\\\=(6^(2x))/(6^x)\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)\\\\=6^(2x-x)=6^x}`