We are given the function:
g(n) = \(3 (\frac{7}{5} )^n\)
We need to find what g(-3) equals.
What the question is asking is what is the resulting value after you plug in -3 as n to the function. Meaning you replace the n that is in the function with -3.
g(-3) = \(3( \frac{7}{5})^{-3}\)
Remember back to the order of operations.
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
For this problem we can keep the fraction as it is (unless you are permitted to use a calculator... if that is the case then just plug all that into a calculator) and keep going to the exponent.
Negative exponents make fractions FLIP. So our fraction will look like this: \((\frac{7}{5})^{-3} = (\frac{5}{7})^{3}\)
Now that we have it without the negative exponent we need to distribute the cubed power to each number in the fraction (which is essentially the same as saying this: \(\frac{5}{7}* \frac{5}{7}* \frac{5}{7}\))
\(\frac{5^{3}}{7^{3}} = \frac{125}{343}\)
We ARE NOT done! We still have this left:
g(-3) = \(3 \frac{125}{343}\)
Multiplying by 3 you get the following:
\(\frac{375}{343}\)
So what does g(-3) equal? This right here:
\(\frac{375}{343}\)
