Simplifying and Evaluating Expressions Using the Power Property of Exponents
Apply the Power of a Power Property to simplify exponential expressions by multiplying exponents. Master this Grade 9 rule for efficient algebra problem-solving.
Key Concepts
New Concept Power of a Power Property: If $m$ and $n$ are real numbers and $x \neq 0$, then $(x^m)^n = x^{mn}$. What’s next Next, you’ll apply this core idea to simplify products and quotients raised to a power, solving practical problems.
Common Questions
What is the Power of a Power Property?
When raising a power to another power, multiply the exponents. For example, (x^3)^4 = x^12 because 3 times 4 equals 12.
How do you simplify (2x^3)^4 using the Power Property?
Apply the power to each factor: 2^4 times (x^3)^4 = 16 times x^12 = 16x^12. Multiply exponents for variables and apply the power to the coefficient.
When does the Power Property apply versus the Product Property?
Power Property: (x^m)^n = x^(mn) for a power raised to a power. Product Property: x^m times x^n = x^(m+n) for multiplying same-base terms.