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Simplify (52)5(5^2)^5 to a single power of 55.

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Full solution

Q. Simplify (52)5(5^2)^5 to a single power of 55.
  1. Identify Base and Exponents: Identify the base and the exponents in (52)5(5^2)^5.\newlineIn (52)5(5^2)^5, 55 is the base raised first to the exponent 22 and then the result is raised to the exponent 55.\newlineBase: 55\newlineFirst Exponent: 22\newlineSecond Exponent: 55
  2. Apply Power of Power Rule: Apply the power of a power rule.\newlineThe power of a power rule states that (am)n=am∗n(a^m)^n = a^{m*n}. Therefore, (52)5(5^2)^5 can be simplified to 52∗55^{2*5}.\newlineCalculation: 52∗5=5105^{2*5} = 5^{10}
  3. Simplify Expression: Simplify the expression. 5105^{10} means 55 is multiplied by itself 1010 times. Final Simplified Form: 5105^{10}

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