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Simplify. Express your answer as the given base raised to a single exponent.\newline(113)3(11^3)^3

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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(113)3(11^3)^3
  1. Recognize expression structure: Step 11: Recognize the expression structure.\newlineWe have (113)3(11^3)^3, which means 1111 raised to the power of 33, and then that result raised to the power of 33 again.
  2. Apply power rule: Step 22: Apply the power of a power rule.\newlineAccording to the rule (am)n=am∗n(a^m)^n = a^{m*n}, we calculate:\newline(113)3=113∗3=119(11^3)^3 = 11^{3*3} = 11^9.
  3. Verify calculation: Step 33: Verify the calculation.\newlineRechecking the power rule: (am)n=am∗n(a^m)^n = a^{m*n} confirms that 113∗311^{3*3} indeed simplifies to 11911^9.

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