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Simplify. Express your answer as the given base raised to a single exponent.\newline(109)3(10^9)^3

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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(109)3(10^9)^3
  1. Identify base and exponents: Identify the base and the exponents in the expression.\newlineIn (109)3(10^9)^3, 1010 is the base raised to the exponent 99, which is then raised to another exponent, 33.\newlineBase: 1010\newlineExponents: 99, 33
  2. Apply power of power property: Apply the power of a power property (am)n=a(m∗n)(a^m)^n = a^{(m*n)}.\newline(109)3=10(9∗3)(10^9)^3 = 10^{(9*3)}\newlineCalculate 9∗3=279*3 = 27
  3. Simplify expression: Simplify the expression by calculating 102710^{27}. 102710^{27} means 1010 multiplied by itself 2727 times, which is a very large number.

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