Remember: [tex](a^b)^c=a^{bc}[/tex] and [tex]\sqrt[n]{a^b}=a^\frac{b}{n}[/tex]
Not sure if you mean
AAA. [tex]f(x)=2(\sqrt[3]{27})^{2x}[/tex]
or
BBB. [tex]2(\sqrt[3]{27^{2x}})[/tex]
Or
CCC. [tex](2\sqrt[3]{27})^{2x}[/tex]
If AAA, go to AAAAAA
If BBB, go to BBBBB
If CCC, go to CCCCC
AAAAAAAAA
[tex]f(x)=2(\sqrt[3]{27})^{2x}[/tex]
Simplify inside parenthaees first
[tex]f(x)=2(\sqrt[3]{3^3})^{2x}[/tex]
[tex]f(x)=2(3)^{2x}[/tex]
[tex]f(x)=2((3)^2)^x[/tex]
[tex]f(x)=2(9)^x[/tex]
The base is 9
BBBBBBBB
[tex]f(x)=2(\sqrt[3]{27^{2x})[/tex]
[tex]f(x)=2(\sqrt[3]{(3^3)^{2x})[/tex]
[tex]f(x)=2(\sqrt[3}{3^{6x}})[/tex]
[tex]f(x)=2(3^\frac{6x}{3})[/tex]
[tex]f(x)=2(3^{2x})[/tex]
[tex]f(x)=2(3^2)^x[/tex]
[tex]f(x)=2(9)^x[/tex]
The base is 9
CCCCCCC
[tex]f(x)=(2\sqrt[3]{27})^{2x}[/tex]
[tex]f(x)=(2\sqrt[3]{3^3})^{2x}[/tex]
[tex]f(x)=(2*3)^{2x}[/tex]
[tex]f(x)=6^{2x}[/tex]
[tex]f(x)=(6^2)^x[/tex]
[tex]f(x)=36^x[/tex]
Base is 36
If it’s [tex]f(x)=2(\sqrt[3]{27})^{2x}[/tex] or [tex]f(x)=2(\sqrt[3]{27^{2x}})[/tex], the base is 9
If it’s [tex]f(x)=(2\sqrt[3]{27})^{2x}[/tex], the base is 36
