%5E4.jpeg "(a^5)^4")
Understanding (a^5)^4
In mathematics, (a^5)^4 represents a power raised to another power. This expression can be simplified using the power of a power rule. This rule states that when raising a power to another power, you multiply the exponents.
The Power of a Power Rule
The power of a power rule is expressed as:
(a^m)^n = a^(m*n)
This means that when you have a base (a) raised to a power (m), and then that entire expression is raised to another power (n), you can simplify it by multiplying the exponents (m and n).
Applying the Rule to (a^5)^4
In our example, we have (a^5)^4. Applying the power of a power rule, we get:
(a^5)^4 = a^(5*4) = a^20
Therefore, (a^5)^4 is equivalent to a^20.
Example
Let's say a = 2. Using the simplified expression, we can calculate the result:
- a^20 = 2^20 = 1,048,576
This demonstrates how simplifying the expression using the power of a power rule can be helpful for calculations.
Summary
In summary, (a^5)^4 can be simplified to a^20 using the power of a power rule. This rule is a fundamental concept in algebra and helps to simplify complex expressions involving exponents.