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Select the equivalent expression.

(9^(6)*7^(-9))^(-4)=?
Choose 1 answer:
(A) 
(9^(24))/(7^(36))
(B) 
(7^(36))/(9^(24))
(C) 
9^(24)*7^(-36)

Select the equivalent expression.\newline(9679)4=(9^{6}\cdot7^{-9})^{-4}=?\newlineChoose 11 answer:\newline(A) 924736\frac{9^{24}}{7^{36}}\newline(B) 736924\frac{7^{36}}{9^{24}}\newline(C) 9247369^{24}\cdot7^{-36}

Full solution

Q. Select the equivalent expression.\newline(9679)4=(9^{6}\cdot7^{-9})^{-4}=?\newlineChoose 11 answer:\newline(A) 924736\frac{9^{24}}{7^{36}}\newline(B) 736924\frac{7^{36}}{9^{24}}\newline(C) 9247369^{24}\cdot7^{-36}
  1. Apply product rule: Apply the power of a product rule, which states that (ab)n=an×bn(ab)^n = a^n \times b^n, to the expression (96×79)4(9^{6}\times7^{-9})^{-4}.\newline(96×79)4=96×(4)×79×(4)(9^{6}\times7^{-9})^{-4} = 9^{6\times(-4)} \times 7^{-9\times(-4)}
  2. Multiply exponents: Multiply the exponents inside the parentheses by the exponent outside the parentheses.\newline9(6(4))×7(9(4))=924×7369^{(6*(-4))} \times 7^{(-9*(-4))} = 9^{-24} \times 7^{36}
  3. Reciprocal of 9249^{24}: Recognize that 9249^{-24} is the reciprocal of 9249^{24}, which can be written as 1924\frac{1}{9^{24}}.\newline924×736=(1924)×7369^{-24} \times 7^{36} = \left(\frac{1}{9^{24}}\right) \times 7^{36}
  4. Rearrange expression: Rearrange the expression to show the division by 9249^{24}.\newline(1924)736=736924\left(\frac{1}{9^{24}}\right) \cdot 7^{36} = \frac{7^{36}}{9^{24}}
  5. Final expression: Match the final expression with the given choices.\newline736/9247^{36} / 9^{24} corresponds to choice (B) (736)/(924)(7^{36})/(9^{24}).

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