The exponent with a single base is - [tex](3)^{\frac{1}{6} }[/tex] and the value of x = 1/6.
We have the following expression - [tex](\frac{3^{\frac{3}{4} }}{3^{\frac{3}{8} } })^{\frac{4}{9} }[/tex]
We have to rewrite this expression as an exponent with a single base - [tex]3^{x}[/tex] and find the value of x.
Simplify the following expression - f(x, y) = [tex]\frac{a^{x} }{a^{y} }[/tex]
In the simplified form, the expression can be written as - f(x, y) = [tex]a^{x-y}[/tex]
We have the following expression - [tex](\frac{3^{\frac{3}{4} }}{3^{\frac{3}{8} } })^{\frac{4}{9} }[/tex]
The expression can be simplified as follows -
[tex](3^{\frac{3}{4} -\frac{3}{8} } )^{\frac{4}{9} } \\\\3^{\frac{3}{8}\times \frac{4}{9} } \\\\(3)^{\frac{1}{6} }[/tex]
Hence, the exponent with a single base - [tex](3)^{\frac{1}{6} }[/tex] and the value of x = 1/6.
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