Respuesta :
The expression for f(x) is 8x+11.
What is an equivalent expression?
An equivalent expression is an expression that has the same value but does not look the same. When you simplify an expression, you're basically trying to write it in the simplest way possible.
For the given situation,
The expression (1/49)^x * (1/7)^(6x+11)
[tex][(\frac{1}{49} )^x] [ (\frac{1}{7} )^{(6x+11) }][/tex]
⇒ [tex][(\frac{1}{7^{2} } )^x] [ (\frac{1}{7} )^{(6x+11) }][/tex]
⇒ [tex][(\frac{1}{7} )^{2x} ] [ (\frac{1}{7} )^{(6x+11) }][/tex]
⇒ [tex]\frac{1}{7} ^{(2x+6x+11)}[/tex] [∵ [tex][a^{n}][a^{m} ] = a^{n+m}[/tex]]
⇒ [tex]\frac{1}{7} ^{(8x+11)}[/tex]
On comparing this expression with [tex]\frac{1}{7} ^{f(x)}[/tex],
we get f(x) as [tex]8x+11[/tex].
Hence we can conclude that the expression for f(x) is 8x+11.
Learn more about equivalent expression here
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