%5E4.jpeg "(2^5/x^2)^4")
Simplifying the Expression (2^5/x^2)^4
This article will explore how to simplify the expression (2^5/x^2)^4. Understanding the rules of exponents is crucial for simplifying this expression.
Understanding the Rules of Exponents
- Power of a Quotient: When raising a fraction to a power, you raise both the numerator and denominator to that power. This can be expressed as: (a/b)^n = a^n / b^n.
- Power of a Power: When raising a power to another power, you multiply the exponents. This can be expressed as: (a^m)^n = a^(m*n).
Applying the Rules
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Applying the Power of a Quotient Rule: (2^5/x^2)^4 = (2^5)^4 / (x^2)^4
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Applying the Power of a Power Rule: (2^5)^4 / (x^2)^4 = 2^(54) / x^(24)
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Simplifying: 2^(54) / x^(24) = 2^20 / x^8
Final Result
Therefore, the simplified expression of (2^5/x^2)^4 is 2^20 / x^8.
Note
It's important to remember that x cannot be equal to 0 because dividing by zero is undefined.