Question 1

Why do we add exponents when multiplying with the same base?

Accepted Answer

Because an exponent counts how many times the base is multiplied. For example, $x^3 = x \cdot x \cdot x$ and $x^2 = x \cdot x$. Multiplying them gives $(x \cdot x \cdot x) \cdot (x \cdot x) = x^5$, so $3 + 2 = 5$.

Question 2

Why can’t we add exponents if the bases are different?

Accepted Answer

The product rule only applies when the bases are identical ($a^m \cdot a^n = a^{m+n}$). An expression like $2^3 \cdot 3^4$ or $x^3 \cdot y^4$ has different bases, so the exponents cannot be added.

Question 3

What is the exponent of a variable without an exponent like $x$?

Accepted Answer

What is the exponent of a variable without an exponent like $x$?

Final Exam

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