Question

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

Answer 1

hint: \(\bf (a^n)^m\implies (a^m)^n\implies (a^{n\cdot m})\qquad thus
\\ \quad \\
2(5)^{2x}\implies 2(5^2)^x\implies 2(5^x)^2\implies 2(5^{2x})\)

Answer 2

think about it \(\bf 2(5)^{2x}\implies \underline{2(5^2)^x}\implies 2(5^x)^2\implies 2(5^{2x})\)

Answer 3

f(x) = 100x?

Answer 4

@jdoe0001

Answer 5

haemmm nope

the 2 is not affected by the exponent, since the 2 is not inside the parentheses

Answer 6

notice \(\bf \bf 2(5)^{2x}\implies {\color{brown}{ 2(5^2)^x }}\implies 2(5^x)^2\implies 2(5^{2x})
\)

Answer 7

it will be \[2(5)^{2x}\]
this will lead to \[2([5^2]^x)\]
so this leads to f(x)=\[2(25)^{x}\]

Answer 8

f(x)=2(25)x

Answer 9

None
2(5)2x = 20x
If you meant 2(5)^2x, then 2(5)^2x = 2(25)x = 50x.