1. The problem asks to write $x^3 \cdot x^3$ without exponents and then fill in the blank for $x^3 \cdot x^3 = x^\square$. 2. Recall the exponent multiplication rule: when multiplying powers with the same base, add the exponents. 3. Using this rule: $$x^3 \cdot x^3 = x^{3+3} = x^6$$ 4. Writing $x^3 \cdot x^3$ without exponents means writing out the multiplication explicitly: $$x^3 = x \cdot x \cdot x$$ So, $$x^3 \cdot x^3 = (x \cdot x \cdot x) \cdot (x \cdot x \cdot x) = x \cdot x \cdot x \cdot x \cdot x \cdot x$$ 5. Therefore, the blank in $x^3 \cdot x^3 = x^\square$ is 6. Final answers: - Without exponents: $x \cdot x \cdot x \cdot x \cdot x \cdot x$ - With exponent: $x^6$