Question
State the product law of exponents.
✓
Answer
State the product law of exponents. If $a$ is any real number and $m, n$ are positive integers, then $a^m \times a^n=a^{m+n}$ By definition, we have $a^m \times a^n=(a \times a \times \ldots m$ factor $) \times(a \times a \times \ldots n$ factor $) a^m \times a^n=a \times a \ldots$ to $(m+n)$ factors $a^m \times a^n$
$=a^{m+n}$ Thus the exponent "product rule" tells us that, when multiplying two powers that have the same base, we can add the exponents.
$=a^{m+n}$ Thus the exponent "product rule" tells us that, when multiplying two powers that have the same base, we can add the exponents.
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