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(a^(3))^(3)*a^(-9) Which of the following expressions is equivalent to the given expression for all a!=0 ? Choose 1 answer: (A) 0 (B) 1 (c) a^(3) (D) a^(18)

(a3)3⋅a−9 \left(a^{3}\right)^{3} \cdot a^{-9} \newlineWhich of the following expressions is equivalent to the given expression for all a≠0 a \neq 0 ?\newlineChoose 11 answer:\newline(A) 00\newline(B) 11\newline(C) a3 a^{3} \newline(D) a18 a^{18}

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Q. (a3)3⋅a−9 \left(a^{3}\right)^{3} \cdot a^{-9} \newlineWhich of the following expressions is equivalent to the given expression for all a≠0 a \neq 0 ?\newlineChoose 11 answer:\newline(A) 00\newline(B) 11\newline(C) a3 a^{3} \newline(D) a18 a^{18}
  1. Simplify expression using power of a power rule: We need to simplify the expression (a3)3⋅a−9(a^{3})^{3}\cdot a^{-9}.\newlineUsing the power of a power rule, (am)n=am⋅n(a^{m})^{n} = a^{m\cdot n}, we can simplify the first part of the expression:\newline(a3)3=a3⋅3=a9(a^{3})^{3} = a^{3\cdot 3} = a^{9}.
  2. Combine exponents using product of powers rule: Now we have a9⋅a−9a^{9}\cdot a^{-9}.\newlineUsing the product of powers rule, am⋅an=am+na^{m}\cdot a^{n} = a^{m+n}, we can combine the exponents:\newlinea9⋅a−9=a9−9=a0a^{9}\cdot a^{-9} = a^{9-9} = a^{0}.
  3. Apply zero exponent rule: According to the zero exponent rule, any non-zero number raised to the power of 00 is 11:a(0)=1,a^{(0)} = 1, where aa is not equal to 00.
  4. Final result and corresponding choice: We have found that the expression (a3)3⋅a−9(a^{3})^{3}\cdot a^{-9} simplifies to 11. Therefore, the equivalent expression is 11, which corresponds to choice (B).

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