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Evaluate. Write your answer as a whole number or as a simplified fraction.\newline6764=\frac{6^{7}}{6^{4}}=

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Full solution

Q. Evaluate. Write your answer as a whole number or as a simplified fraction.\newline6764=\frac{6^{7}}{6^{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, (67)/(64)(6^{7})/(6^{4}) becomes 67−46^{7-4}.
  2. Subtract Exponents: Subtract the exponents. 7−4=37 - 4 = 3 So, 6(7−4)6^{(7-4)} becomes 636^3.
  3. Calculate Result: Calculate 636^3. \newline63=6×6×6=2166^3 = 6 \times 6 \times 6 = 216

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