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Simplify. Express your answer as the given base raised to a single exponent.\newline(38)9(3^8)^9

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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(38)9(3^8)^9
  1. Identify base and exponents: Identify the base and the exponents in the expression.\newlineIn (38)9(3^8)^9, 33 is the base, raised first to the exponent 88 and then to 99.\newlineBase: 33\newlineExponents: 88, 99
  2. Apply power of power property: Apply the power of a power property: (am)n=a(m∗n)(a^m)^n = a^{(m*n)}.\newline(38)9=3(8∗9)(3^8)^9 = 3^{(8*9)}\newline= 3723^{72}
  3. Check simplification: Check if 3723^{72} is simplified and expressed as a single exponent.\newlineYes, 3723^{72} is already in the simplest form with a single exponent.

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