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Evaluate. Write your answer as a whole number or as a simplified fraction.\newline323^{2}⋅\cdot323^{2}=□\Box

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Sin, cos, and tan of special anglesright chevron icon

Full solution

Q. Evaluate. Write your answer as a whole number or as a simplified fraction.\newline323^{2}⋅\cdot323^{2}=□\Box
  1. Understand the problem: Understand the problem.\newlineWe need to find the value of 32⋅323^{2} \cdot 3^{2}. This involves using the laws of exponents to simplify the expression.
  2. Apply exponent law for multiplication: Apply the law of exponents for multiplication.\newlineWhen multiplying two exponents with the same base, we add the exponents: am⋅an=am+na^{m} \cdot a^{n} = a^{m+n}.\newlineSo, 32⋅32=32+23^{2} \cdot 3^{2} = 3^{2+2}.
  3. Simplify the exponent: Simplify the exponent.\newline32+2=343^{2+2} = 3^{4}.
  4. Calculate the value: Calculate the value of 343^{4}.\newline34=3⋅3⋅3⋅3=813^{4} = 3 \cdot 3 \cdot 3 \cdot 3 = 81.

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