%5E3%2F4.jpeg "(16x^16)^3/4")
Simplifying (16x^16)^3/4
This problem involves simplifying an expression with exponents. Let's break it down step by step:
Understanding the Properties of Exponents
- Product of Powers: (x^m) * (x^n) = x^(m+n)
- Power of a Power: (x^m)^n = x^(m*n)
- Fractional Exponent: x^(1/n) = n√x (nth root of x)
Simplifying the Expression
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Apply the Power of a Power rule: (16x^16)^(3/4) = 16^(3/4) * (x^16)^(3/4)
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Simplify the numerical term: 16^(3/4) = (2^4)^(3/4) = 2^(4 * (3/4)) = 2^3 = 8
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Simplify the variable term: (x^16)^(3/4) = x^(16 * (3/4)) = x^12
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Combine the simplified terms: 8 * x^12 = 8x^12
Final Answer
Therefore, the simplified form of (16x^16)^(3/4) is 8x^12.