## anonymous one year ago Please help Meh Which of the following options is an equivalent function to f(x) = 3(2)^3^x? (both 3 and x are listed as exponents :)

1. anonymous

2. phi

is it $f(x) = 3(2)^{3^x}$?

3. phi

or $f(x)= 3(2)^{3x}$ ?

4. phi

we can't do much with the first. the second can be written as $f(x)= 3(2^3)^x = 3\cdot 8^x$

5. anonymous

whats the difference between the two equations? @phi sorry my mum called me

6. phi

the first one has $$3^x$$ as the exponent. the second way has 3x as the exponent. the first way can't be simplified. the second way can be, using the rule $a^{bc}= (a^b)^c$

7. anonymous

(3x) is an exponent, they are both together and the same location/size... @phi

8. phi

that means you can write the 2^(3x) as either $(2^x)^3$ or $(2^3)^x$ the second way means $(2\cdot 2\cdot 2)^x$ or $8^x$

9. phi

and we still have a 3 out front so you could write the expression 3 * 2^(3x) as 3*8^x

10. phi

Does that match any of your options?