## anonymous one year ago 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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1. anonymous

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

2. anonymous

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

3. anonymous

f(x) = 100x?

4. anonymous

@jdoe0001

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

f(x)=2(25)x

9. fairygirl0404

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