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Evaluate. Write your answer as a whole number or as a simplified fraction.\newline3935=□\frac {3^{9}}{3^{5}}=\square

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Full solution

Q. Evaluate. Write your answer as a whole number or as a simplified fraction.\newline3935=□\frac {3^{9}}{3^{5}}=\square
  1. Apply quotient rule: Apply the quotient rule for exponents.\newlineThe quotient rule states that when dividing like bases with exponents, you subtract the exponents: am/an=am−na^{m}/a^{n} = a^{m-n}.\newlineSo, (39)/(35)(3^{9})/(3^{5}) becomes 39−53^{9-5}.
  2. Subtract exponents: Subtract the exponents.\newline9−5=49 - 5 = 4\newlineSo, 39−53^{9-5} becomes 343^4.
  3. Calculate 343^4: Calculate 343^4.\newline34=3×3×3×3=813^4 = 3 \times 3 \times 3 \times 3 = 81

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