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Which expression is equivalent to (97)3(9^7)^3?\newlineChoices:\newline(A) 1910\frac{1}{9^{10}}\newline(B) 1921\frac{1}{9^{21}}\newline(C) 9109^{10}\newline(D) 9219^{21}

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Q. Which expression is equivalent to (97)3(9^7)^3?\newlineChoices:\newline(A) 1910\frac{1}{9^{10}}\newline(B) 1921\frac{1}{9^{21}}\newline(C) 9109^{10}\newline(D) 9219^{21}
  1. Apply Power Rule: Apply the power of a power rule.\newlineThe power of a power rule states that (am)n=a(m∗n)(a^m)^n = a^{(m*n)}. We will apply this rule to the expression (97)3(9^7)^3.\newline(97)3=9(7∗3)(9^7)^3 = 9^{(7*3)}
  2. Multiply Exponents: Multiply the exponents.\newlineNow we multiply the exponents 77 and 33 to find the new exponent for the base 99.\newline9(7∗3)=9219^{(7*3)} = 9^{21}
  3. Match with Choices: Match the result with the given choices.\newlineWe have found that (97)3=921(9^7)^3 = 9^{21}. Now we look at the choices to find the equivalent expression.\newlineThe correct choice is (D) 9219^{21}.

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