Product Property of Exponents
Multiply powers with the same base by adding exponents: x^m times x^n equals x^(m+n). Apply this Grade 9 exponent rule to simplify algebraic expressions.
Key Concepts
Property If $m$ and $n$ are real numbers and $x \neq 0$, then $x^m \cdot x^n = x^{m+n}$.
Examples $b^4 \cdot b^8 \cdot b^2 = b^{4+8+2} = b^{14}$ $p^3 \cdot p^6 \cdot q^5 \cdot q^9 = p^{3+6} \cdot q^{5+9} = p^9q^{14}$ $10^4 \cdot 10^5 = 10^{4+5} = 10^9$.
Explanation When you multiply terms with the same base, just keep that base and add the exponents together! It's like combining two collections of the same thing. If you have a group of 3 apples ($a^3$) and another group of 5 apples ($a^5$), you don't magically get 15 apples; you just have a bigger group of 8 apples ($a^8$).
Common Questions
What is the Product Property of Exponents and when does it apply?
It is a rule that holds for all values in its domain. Apply it whenever you see the matching pattern in an algebraic expression or equation.
How do you apply the product property of exponents step by step?
Identify the pattern, substitute into the formula, simplify each part in order, and combine the results.
What mistakes should you avoid with the product property of exponents?
Misidentifying which part of the expression the rule applies to, and forgetting conditions like nonzero bases or non-negative radicands.