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Evaluate. Write your answer as a whole number or as a simplified fraction.\newline(38)/(34)=(3^{8})/(3^{4})=

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Full solution

Q. Evaluate. Write your answer as a whole number or as a simplified fraction.\newline(38)/(34)=(3^{8})/(3^{4})=
  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, (38)/(34)(3^{8})/(3^{4}) becomes 38−43^{8-4}.
  2. Subtract Exponents: Subtract the exponents.\newline8−4=48 - 4 = 4\newlineSo, 3(8−4)3^{(8-4)} 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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