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(33⋅43)2(3^3 \cdot 4^3)^2

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Full solution

Q. (33⋅43)2(3^3 \cdot 4^3)^2
  1. Apply Product Rule: Apply the power of a product rule which states that (ab)2=a2b2 (ab)^2 = a^2b^2 . (33⋅43)2=(33)2⋅(43)2 (3^3\cdot4^3)^2 = (3^3)^2\cdot(4^3)^2 .
  2. Apply Power Rule: Apply the power of a power rule which states that a^m)^n = a^{(mn)}\.\$(3^3)^2 = 3^{(3\cdot2)} = 3^6(43)2=4(3⋅2)=46(4^3)^2 = 4^{(3\cdot2)} = 4^6
  3. Calculate Exponents: Calculate the value of 363^6 and 464^6.\newline36=3⋅3⋅3⋅3⋅3⋅3=7293^6 = 3\cdot3\cdot3\cdot3\cdot3\cdot3 = 729\newline46=4⋅4⋅4⋅4⋅4⋅4=40964^6 = 4\cdot4\cdot4\cdot4\cdot4\cdot4 = 4096
  4. Multiply Results: Multiply the results from Step 33. 729⋅4096729 \cdot 4096
  5. Perform Final Multiplication: Perform the multiplication to find the final answer. 729⋅4096=2,985,984729 \cdot 4096 = 2,985,984

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