How to solve $5^n - 5^{n-3} = 5^{n-3} *124$

Question

how is $$5^n - 5^{n-3} = 5^{n-3} *124$$

Can anybody provide a step by step solution.I will greatly appreciate if any online source for such material is provided.

Regards

Answer 1

Recall that $$a^b\cdot a^c = a^{b+c}$$ So here we use the fact that $$5^n = 5^{(n - 3)+ 3} = 5^{n -3}\cdot 5^3$$

Factor out $5^{n-3}$ from the left hand side:

$$\begin{align}5^n - 5^{n-3} & = \underbrace{\color{blue}{5^{n-3}}\cdot 5^3}_{\large =\,5^n} - \color{blue}{5^{n-3}}\cdot 1 \\ \\ & = \color{blue}{5^{n-3}}(5^3 - 1) \\ \\& = 5^{n - 3}\cdot 124\end{align}$$

For (free) online tutorials dealing with equations and exponents, see the Khan Academy.