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Simplify. Express your answer as the given base raised to a single exponent.\newline(48)2(4^8)^2

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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(48)2(4^8)^2
  1. Recognize expression structure: Step 11: Recognize the expression structure.\newline(48)2(4^8)^2 involves an exponentiation of an exponentiation.\newlineBase: 44\newlineExponents: 8,28, 2
  2. Apply power of power rule: Step 22: Apply the power of a power rule.\newline(48)2=4(8∗2)(4^8)^2 = 4^{(8*2)}\newline=416= 4^{16}
  3. Check calculation: Step 33: Check the calculation.\newline4164^{16} is the simplified form of (48)2(4^8)^2, following the rule (am)n=a(m∗n)(a^m)^n = a^{(m*n)}.

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