Answer:
Step-by-step explanation:
To find the expression for 5/a, you first need to solve the equation 5=a^x for a. To solve for a, raise both sides of the equation to the 1/x power.
5=a^x
5^(1/x)=(a^x)^(1/x) (now multipy exponents)
5^(1/x)=a (x*1/x = 1 - the exponent on a)
Now that the equation is solved for a, substitute the left side of the equation into 5/a. So,
5/a = 5/5^(1/x) (since the bases are the same, 5, subtract the exponents; note that the exponent in the numerator = 1)
5/a = 5^(1 - 1/x) (subtract by getting lcd, x)
5/a = 5^((x-1)/x)
Just to show you that this works: Let a = 25 and x = 1/2.
We know that 5 = a^x = 25^(1/2) = sqrt(25)=5.
Now, 5/a should equal 5/25 = 1/5, so let's plug the numbers into the new expression.
5/a = 5^((.5-1)/.5) (I'm using .5 instead of 1/2 so it's not so many parentheses.)
