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

Step 1: Understand the meaning: Understand the meaning of the fifth root of b to the ninth power. The fifth root of b to the ninth power is written as root(5)(b^(9)). This means we are looking for a number that, when raised to the fifth power, gives b to the ninth power.Step 2: Simplify the expression: Simplify the expression using the property of exponents that states the nth root of a number raised to the mth power is equal to that number raised to the m/n power. root(5)(b^(9)) is equivalent to b^((9)/(5)).Step 3: Check other options: Check the other options to see if they are equivalent. Option B suggests b^((5)/(9)), which is not equivalent because it implies the ninth root of b to the fifth power, not the fifth root of b to the ninth power.Step 4: Check option C: Check option C. Option C suggests (b^(5))^((1)/(9)). This is not equivalent because it implies taking b to the fifth power first and then taking the ninth root of the result, which is not the same as the fifth root of b to the ninth power.Step 5: Conclude the solution: Conclude that option D, ＂None of the above,＂ is incorrect because we have found that option A is equivalent to the original expression.

Which expressions are equivalent to $\sqrt[5]{b^{9}}$ ? $\newline$ Choose all answers that apply: $\newline$ A $b^{\frac{9}{5}}$ $\newline$ B $b^{\frac{5}{9}}$ $\newline$ C $\left(b^{5}\right)^{\frac{1}{9}}$ $\newline$ D None of the above

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Which expressions are equivalent to $\sqrt[5]{b^{9}}$ ? $\newline$ Choose all answers that apply: $\newline$ A $b^{\frac{9}{5}}$ $\newline$ B $b^{\frac{5}{9}}$ $\newline$ C $\left(b^{5}\right)^{\frac{1}{9}}$ $\newline$ D None of the above