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Simplify. Express your answer as the given base raised to a single exponent.\newline(85)4(8^5)^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(85)4(8^5)^4
  1. Identify Base and Exponents: Identify the base and the exponents in the expression.\newlineIn (85)4(8^5)^4, 88 is the base raised to the exponent 55, which is then raised to another exponent 44.\newlineBase: 88\newlineExponents: 55, 44
  2. Apply Power of Power Property: Apply the power of a power property to simplify (85)4(8^5)^4.(85)4=8(5∗4)(8^5)^4 = 8^{(5*4)}=820= 8^{20}
  3. Check Calculation: Check the calculation for any errors.\newline55 multiplied by 44 equals 2020, so 8208^{20} is correct.

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