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Evaluate. Write your answer as a whole number or as a simplified fraction.\newline42⋅42=□4^{2} \cdot 4^{2} = \square

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Full solution

Q. Evaluate. Write your answer as a whole number or as a simplified fraction.\newline42⋅42=□4^{2} \cdot 4^{2} = \square
  1. Apply Rule of Exponents: Use the rule of exponents that says am⋅an=am+na^{m}\cdot a^{n} = a^{m+n}. So, 42⋅424^{2}\cdot 4^{2} can be simplified to 42+24^{2+2}.
  2. Calculate New Exponent: Calculate the new exponent: 2+2=42+2=4. So, we have 444^{4}.
  3. Evaluate Exponential Expression: Calculate 44=4×4×4×4=2564^{4} = 4 \times 4 \times 4 \times 4 = 256.

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