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Simplify. Express your answer as the given base raised to a single exponent.\newline(58)9(5^8)^9

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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(58)9(5^8)^9
  1. Identify Base and Exponents: Identify the base and the exponents in the expression.\newlineBase: 55\newlineExponents: 8,98, 9
  2. Apply Power of Power Rule: Apply the power of a power rule: (am)n=a(m∗n)(a^m)^n = a^{(m*n)}.\newlineCalculation: (58)9=5(8∗9)(5^8)^9 = 5^{(8*9)}
  3. Perform Exponent Multiplication: Perform the multiplication of the exponents.\newlineCalculation: 8×9=728 \times 9 = 72
  4. Write Final Expression: Write the final expression with the calculated exponent.\newlineFinal Expression: 5725^{72}

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