%5E24.jpeg "(a^8)^24")
Simplifying Exponential Expressions: (a^8)^24
In mathematics, understanding how to simplify exponential expressions is crucial. One common type of problem involves raising an exponent to another exponent, as seen in the expression (a^8)^24.
Let's break down the steps to simplify this:
The Rule of Exponents
The key principle at play here is the rule of exponents for powers of powers. This rule states that when raising a power to another power, you multiply the exponents.
Mathematically: (a^m)^n = a^(m*n)
Applying the Rule
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Identify the base and the exponents: In our example, the base is a and we have two exponents: 8 and 24.
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Multiply the exponents: According to the rule, we multiply the exponents: 8 * 24 = 192.
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Write the simplified expression: The simplified form of (a^8)^24 is a^192.
Conclusion
Therefore, (a^8)^24 simplifies to a^192. This principle applies to any base and exponents, making it a fundamental tool for simplifying complex exponential expressions.