%5E2.jpeg "(a^2b^3)^2")
Understanding (a^2b^3)^2
The expression (a^2b^3)^2 is a simple example of how exponents work with multiple variables. Let's break down the components and learn how to simplify it.
Understanding the Components
- a^2: This represents 'a' multiplied by itself twice (a * a).
- b^3: This represents 'b' multiplied by itself three times (b * b * b).
- ( )^2: This indicates that the entire expression inside the parentheses is being squared, meaning it's being multiplied by itself.
Simplifying the Expression
To simplify (a^2b^3)^2, we can apply the following rules:
- Exponent Rule: When raising a power to another power, we multiply the exponents.
- Distributive Property: The exponent applies to each individual factor within the parentheses.
Applying these rules, we get:
(a^2b^3)^2 = (a^2)^2 * (b^3)^2
Now, applying the exponent rule:
(a^2)^2 * (b^3)^2 = a^(22) * b^(32)
Finally, simplifying the exponents:
a^(22) * b^(32) = a^4 * b^6
Final Result
Therefore, the simplified form of (a^2b^3)^2 is a^4b^6.
Key Points
- The exponent rule is crucial for simplifying expressions with exponents raised to other exponents.
- Remember to apply the exponent to each factor within the parentheses.
- This simplification process is applicable to any similar expressions involving multiple variables and exponents.