Question

9e^2f=49 solve for e. please and thank you!

Answer 1

First, divide both sides by 9. You have:
e^2f=49/9
To get rid of the exponent on the e, take both sides to the reciprocol power, which is 1/2f.
If you have (e^2f)^(1/2f) you can multiply the exponents, as this isa property of exponents. 2f*(1/2f)=2f/2f=1
So taking this side to that power gives us e^1, or simply e.
Now, let's try the other side.
(49/9)^(1/2f)
First, we will distribute the exponent to both terms, another property of exponents.
(49^(1/2f))/(9^(1/2f))
Just as you can multiply the exponents as you did previously, you can also split two multiplied exponents.
((49^(1/2))^1/f)/((9^(1/2))^(1/f))
Taking something to the 1/2 power is the same as square rooting it. We can simplify using this information.
(7^(1/f))/(3^(1/f))
This is the simplest form our answer can be in. Also, since this side is equivalent to e, it is clearly our answer.
e=(7^(1/f))/(3^(1/f))