Question

What does g(n) equal

Answer 1

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: 

$\frac{375}{343}$