Which of the following options is an equivalent function to f(x) = 2(5)2x? f(x) = 50x f(x) = 100x f(x) = 2(25)x f(x) = 4(25)x

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Which of the following options is an equivalent function to f(x) = 2(5)2x? f(x) = 50x f(x) = 100x f(x) = 2(25)x f(x) = 4(25)x

Algebra
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hint: \(\bf (a^n)^m\implies (a^m)^n\implies (a^{n\cdot m})\qquad thus \\ \quad \\ 2(5)^{2x}\implies 2(5^2)^x\implies 2(5^x)^2\implies 2(5^{2x})\)
think about it \(\bf 2(5)^{2x}\implies \underline{2(5^2)^x}\implies 2(5^x)^2\implies 2(5^{2x})\)
f(x) = 100x?

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haemmm nope the 2 is not affected by the exponent, since the 2 is not inside the parentheses
notice \(\bf \bf 2(5)^{2x}\implies {\color{brown}{ 2(5^2)^x }}\implies 2(5^x)^2\implies 2(5^{2x}) \)
it will be \[2(5)^{2x}\] this will lead to \[2([5^2]^x)\] so this leads to f(x)=\[2(25)^{x}\]
f(x)=2(25)x
None 2(5)2x = 20x If you meant 2(5)^2x, then 2(5)^2x = 2(25)x = 50x.

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