Question

Medal and Fan for answer!
When you are doing exponential functions, how would you go about solving this?
4^x+3. How do you involve the three in this equation. Say we plugged in -3 as the x. 4^-3+3. What would be the answer?

Answer 1

please note that:
\[4^{-3}+3=\frac{ 1 }{ 4^{3} }+3=\frac{ 1 }{ 64 }+3=\frac{ 1+64*3 }{ 64 }=\]
\[=\frac{ 1+192 }{ 64 }=\frac{ 193 }{ 64 }\]

Answer 2

How does it jump from that?

Answer 3

when you have a power with a negative exponent, then that power goes to denominator with the same exponent but reversed sign.
for example:
\[2^{-5}=\frac{ 1 }{ 2^{5} }\]

Answer 4

How do you convert a fraction back into an exponent?

Answer 5

Like how you have 193/64. Is it possible to convert this back into an exponent?

Answer 6

in general no, it is necessary to perform the factorization in prime numbers. for example, I know that:
\[64=2^{6}\]
and 193 is a prime number, so without any other infromation, your answer is negative

Answer 7

Thanks, that helped alot.

Answer 8

Thanks!