Problem 53 of 7
Explain why rational exponent rule (ab)^(p/q) = a^(p/q) * b^(p/q) preserves exponent laws.
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use (a^(1/n))^n=a.
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Explanation must connect rational exponent notation to exponent properties.
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Solution
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1. Interpret the rational exponent as a root and power.
2. Apply the relevant exponent law.
3. Connect the result back to the radical meaning.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Circular statement that laws work because they work.