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Which expressions are equivalent to (b^(2))^((1)/(9)) ? Choose all answers that apply: A (b^(-(1)/(9)))^(2) B (b^((1)/(9)))^(2) c. (b^((1)/(2)))^(9) D None of the above

Which expressions are equivalent to (b2)19 \left(b^{2}\right)^{\frac{1}{9}} ?\newlineChoose all answers that apply:\newlineA (b−19)2 \left(b^{-\frac{1}{9}}\right)^{2} \newlineB (b19)2 \left(b^{\frac{1}{9}}\right)^{2} \newlineC (b12)9 \left(b^{\frac{1}{2}}\right)^{9} \newlineD None of the above

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Q. Which expressions are equivalent to (b2)19 \left(b^{2}\right)^{\frac{1}{9}} ?\newlineChoose all answers that apply:\newlineA (b−19)2 \left(b^{-\frac{1}{9}}\right)^{2} \newlineB (b19)2 \left(b^{\frac{1}{9}}\right)^{2} \newlineC (b12)9 \left(b^{\frac{1}{2}}\right)^{9} \newlineD None of the above
  1. Determine Exponent Simplification: We need to determine which of the given options are equivalent to the expression (b2)(19)(b^{2})^{(\frac{1}{9})}. According to the properties of exponents, when we raise a power to another power, we multiply the exponents. So, (b2)(19)(b^{2})^{(\frac{1}{9})} simplifies to b2∗(19)b^{2*(\frac{1}{9})}, which is b29b^{\frac{2}{9}}.
  2. Evaluate Option A: Now let's evaluate each option to see if it simplifies to b29b^{\frac{2}{9}}.\newlineOption A: (b−(19))2(b^{-\left(\frac{1}{9}\right)})^{2} simplifies to b−29b^{-\frac{2}{9}}, which is not equivalent to b29b^{\frac{2}{9}} because the exponent is negative.
  3. Evaluate Option B: Option B: (b(1/9))2(b^{(1/9)})^{2} simplifies to b2/9b^{2/9}, which is equivalent to our original expression (b2)(1/9)(b^{2})^{(1/9)}.
  4. Evaluate Option C: Option C: (b(1/2))9(b^{(1/2)})^{9} simplifies to b9/2b^{9/2}, which is not equivalent to b2/9b^{2/9} because the exponent is much larger and not a reciprocal.
  5. Evaluate Option D: Option D: None of the above is not correct because we have found that Option B is equivalent to the original expression.

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