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
$a^m \times a^n = (a \times a \times ... m factor) \times (a \times a \times ... n factor)$
$a^m \times a^n = a \times a ... to (m + n) factors$
$a^m \times a^n = a^{m + n}$
Thus the exponent "product rule" tells us that, when multiplying two powers that have the same base, we can add the exponents.
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
$a^m \times a^n = (a \times a \times ... m factor) \times (a \times a \times ... n factor)$
$a^m \times a^n = a \times a ... to (m + n) factors$
$a^m \times a^n = a^{m + n}$
Thus the exponent "product rule" tells us that, when multiplying two powers that have the same base, we can add the exponents.
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