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Simplify. Express your answer as the given base raised to a single exponent.\newline(22)5(2^2)^5

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Power of a power: integer basesright chevron icon

Full solution

Q. Simplify. Express your answer as the given base raised to a single exponent.\newline(22)5(2^2)^5
  1. Recognize expression structure: Step 11: Recognize the expression structure.\newlineWe have 22)5 whichmeans$22^2)^5\, which means \$2 raised to the power of 22, and then that result raised to the power of 55.
  2. Apply power property: Step 22: Apply the power of a power property.\newlineUsing the rule (am)n=am∗n(a^m)^n = a^{m*n}, we calculate:\newline(22)5=22∗5(2^2)^5 = 2^{2*5}
  3. Perform multiplication: Step 33: Perform the multiplication.\newline2×5=102\times5 = 10\newlineSo, (22)5=210(2^2)^5 = 2^{10}

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