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Simplify. Express your answer as the given base raised to a single exponent.\newline(38)4(3^8)^4

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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)4(3^8)^4
  1. Recognize expression structure: Step 11: Recognize the expression structure.\newlineWe have (38)4(3^8)^4, where 33 is the base and 88 and 44 are the exponents.
  2. Apply power of power rule: Step 22: Apply the power of a power rule.\newline(38)4=3(8∗4)(3^8)^4 = 3^{(8*4)}\newline=332= 3^{32}
  3. Check calculation: Step 33: Check the calculation.\newline88 multiplied by 44 indeed equals 3232, so 3323^{32} is correct.

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