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Simplify. Express your answer as a single term using exponents.\newline76667669\frac{766^6}{766^9}

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Full solution

Q. Simplify. Express your answer as a single term using exponents.\newline76667669\frac{766^6}{766^9}
  1. Identify base and exponents: Step 11: Identify the base and the exponents in the numerator and denominator. In 7666766^6, 766766 is the base raised to the exponent 66. In 7669766^9, 766766 is the base raised to the exponent 99.
  2. Apply quotient of powers: Step 22: Apply the quotient of powers property, which states am/an=a(m−n)a^m / a^n = a^{(m-n)}. Calculate 7666/7669=766(6−9)766^6 / 766^9 = 766^{(6-9)}.
  3. Perform subtraction in exponent: Step 33: Perform the subtraction in the exponent, 6−9=−36 - 9 = -3. So, 7666/7669=766−3766^6 / 766^9 = 766^{-3}.

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