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Simplify. Express your answer as a single term using exponents. \newline63626369\frac{636^2}{636^9}

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Full solution

Q. Simplify. Express your answer as a single term using exponents. \newline63626369\frac{636^2}{636^9}
  1. Identify base and exponents: Step 11: Identify the base and the exponents in the numerator and denominator. In 6362636^2, 636636 is the base raised to the exponent 22. In 6369636^9, 636636 is the base raised to the exponent 99.
  2. Apply quotient of powers rule: Step 22: Apply the quotient of powers rule, which states that am/an=a(m−n)a^m / a^n = a^{(m-n)}. Here, calculate 6362/6369=636(2−9)636^2 / 636^9 = 636^{(2-9)}.
  3. Perform subtraction in exponent: Step 33: Perform the subtraction in the exponent, 2−9=−72 - 9 = -7. So, 6362/6369636^2 / 636^9 simplifies to 636−7636^{-7}.

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