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Simplify. Express your answer as the given base raised to a single exponent.\newline(123)6(12^3)^6

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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(123)6(12^3)^6
  1. Recognize expression structure: Step 11: Recognize the expression structure.\newlineWe have (123)6(12^3)^6, which means 1212 raised to the power of 33, and then that result raised to the power of 66.
  2. Apply power of 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(123)6=123∗6(12^3)^6 = 12^{3*6}\newline= 121812^{18}
  3. Check final expression: Step 33: Check the final expression.\newlineWe simplified (123)6(12^3)^6 to 121812^{18}, which is 1212 raised to a single exponent.

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