It looks like you're working with an equation involving exponents and variables. Let's clarify the equation and solve it step by step.

Given Equation:

$a \cdot a^3 = a$

Step 1: Simplify the left side of the equation

Using the property of exponents $(a^m \cdot a^n = a^{m+n})$, we can simplify the left side: $a \cdot a^3 = a^{1+3} = a^4$ So the equation becomes: $a^4 = a$

Step 2: Solve the equation

To solve $a^4 = a$, we can factor the equation: $a^4 - a = 0$ Factor out $a$: $a(a^3 - 1) = 0$ This equation has two possible solutions:

1. $a = 0$
2. $a^3 - 1 = 0$

For the second part, $a^3 - 1 = 0$, solve for $a$: $a^3 = 1$ Taking the cube root of both sides: $a = 1$

Final Answer:

The solutions are: $a = 0 \quad \text{or} \quad a = 1$

Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:

1. What happens if the equation was $a \cdot a^2 = a$?
2. How do you solve equations with higher powers of $a$?
3. What are the general steps to factor polynomials?
4. Can you solve $a^5 = a$?
5. How would you solve $a^3 = -1$?

Tip: Always check your final answer by substituting it back into the original equation to verify it works.