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Write the expression as a single power of 99.\newline(9−3)(912)=(9^{-3})(9^{12})=

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Full solution

Q. Write the expression as a single power of 99.\newline(9−3)(912)=(9^{-3})(9^{12})=
  1. Apply Law of Exponents: Apply the law of exponents for multiplying powers with the same base.\newlineAccording to the law of exponents, am⋅an=am+na^m \cdot a^n = a^{m+n} when multiplying two exponents with the same base.\newlineHere, we have 9−3⋅9129^{-3} \cdot 9^{12}, so we add the exponents: −3+12-3 + 12.
  2. Add Exponents: Perform the addition of the exponents.\newlineCalculating the sum of the exponents gives us −3+12=9-3 + 12 = 9.
  3. Apply to Base: Apply the sum of the exponents to the base.\newlineNow we have 999^9, which is the simplified form of the original expression.

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