%5E6-x-5%5E-9.jpeg "(5^2)^6 X 5^-9")
Simplifying Exponents: (5^2)^6 x 5^-9
This expression involves exponents and their properties. Let's break down the steps to simplify it:
Understanding the Properties
- Power of a Power: When raising a power to another power, we multiply the exponents. For example, (x^m)^n = x^(m*n).
- Negative Exponents: A negative exponent indicates the reciprocal of the base raised to the positive version of that exponent. For example, x^-n = 1/x^n.
Applying the Properties
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Simplify the first term: (5^2)^6 = 5^(2*6) = 5^12
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Combine the terms: We now have 5^12 * 5^-9
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Apply the rule for multiplication of exponents with the same base: When multiplying exponents with the same base, we add the powers. So, 5^12 * 5^-9 = 5^(12-9) = 5^3
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Calculate the final result: 5^3 = 5 * 5 * 5 = 125
Final Answer
Therefore, (5^2)^6 x 5^-9 simplifies to 125.