Which expressions are equivalent to root(5)(b^(9)) ? Choose all answers that apply: A b^((9)/(5)) B b^((5)/(9)) C (b^(5))^((1)/(9)) D None of the above

Question

Which expressions are equivalent to  root(5)(b^(9)) ? Choose all answers that apply: A  b^((9)/(5)) B  b^((5)/(9)) C  (b^(5))^((1)/(9)) D None of the above

Bytelearn · Accepted Answer

Understand given expression: Understand the given expression. The given expression is root(5)(b^(9)), which means the 5th root of b raised to the 9th power. We need to find which of the given options are equivalent to this expression.Analyze option A: Analyze option A. Option A is b^((9)/(5)). This expression represents b raised to the power of 9/5. The 5th root of b^9 can be written as (b^9)^(1/5), which simplifies to b^(9/5) because when you raise a power to a power, you multiply the exponents. Therefore, option A is equivalent to the given expression.Analyze option B: Analyze option B. Option B is b^((5)/(9)). This expression represents b raised to the power of 5/9. This is not equivalent to the 5th root of b^9 because the exponent here is inverted. Therefore, option B is not equivalent to the given expression.Analyze option C: Analyze option C. Option C is (b^(5))^((1)/(9)). This expression represents b raised to the 5th power and then taking the 9th root of the result. When you take the 9th root of b^5, you get b^(5/9), which is not equivalent to the 5th root of b^9. Therefore, option C is not equivalent to the given expression.Analyze option D: Analyze option D. Option D states ＂None of the above,＂ which implies that none of the previous options are equivalent to the given expression. Since we have already established that option A is equivalent, option D is incorrect.

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