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Simplify. Express your answer as the given base raised to a single exponent.\newline(42)8(4^2)^8

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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(42)8(4^2)^8
  1. Recognize Structure: Step 11: Recognize the structure of the expression.\newline(42)8(4^2)^8 involves a power raised to another power.\newlineBase: 44, First exponent: 22, Second exponent: 88
  2. Apply Power Rule: Step 22: Apply the power of a power rule, which states (am)n=am∗n(a^m)^n = a^{m*n}.\newline(42)8=42∗8(4^2)^8 = 4^{2*8}\newline= 4164^{16}
  3. Check Simplification: Step 33: Check if 4164^{16} is simplified to a single exponent.\newlineYes, 4164^{16} is already in the form of a base raised to a single exponent.

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