%5E4.jpeg "(2a^4)^4")
Simplifying (2a^4)^4
In mathematics, simplifying expressions is a fundamental skill. One common type of expression involves raising a power to another power. This is known as the power of a power rule. Let's look at how to simplify the expression (2a^4)^4.
Applying the Power of a Power Rule
The power of a power rule states that when raising a power to another power, you multiply the exponents.
In our expression, we have:
- (2a^4) as the base, which is raised to the power of 4.
Applying the rule, we get:
(2a^4)^4 = 2^(44) * a^(44)
Simplifying Further
Now we simplify the exponents:
(2a^4)^4 = 2^16 * a^16
Finally, we can calculate 2^16:
(2a^4)^4 = 65,536a^16
Conclusion
Therefore, the simplified form of (2a^4)^4 is 65,536a^16. This illustrates the power of the power of a power rule, making it easy to simplify expressions involving multiple exponents.