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

Understand Properties: To find the equivalent expressions for the fifth root of b to the ninth power, we need to understand the properties of exponents and roots. The fifth root of b to the ninth power can be written as (b^9)^(1/5).Evaluate Option A: Now let's evaluate each option given: A) (b^(5))^((1)/(9)) can be simplified using the property (a^m)^n = a^(m*n), which gives us b^(5*(1/9)) = b^(5/9).Option B: B) The option ＂B＂ is just the letter ＂B＂ and does not represent any mathematical expression, so it cannot be equivalent to root(5)(b^(9)).Evaluate Option C: C) b^((9)/(5)) is already in the form of b^(m/n), but it is not equivalent to (b^9)^(1/5) because 9/5 is not equal to 1/5.Consider Option D: D) ＂None of the above＂ is an option to consider only if none of the other options (A, B, C) are correct. Since we have found that option A is equivalent to root(5)(b^(9)), option D is not correct.Identify Equivalent Expression: Therefore, the only expression equivalent to root(5)(b^(9)) is option A, which is b^(5/9).

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

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

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Q. Which expressions are equivalent to

\sqrt[5]{b^{9}}

\newline

Choose all answers that apply:

\newline

(A)

(b^{5})^{\frac{1}{9}}

\newline

(B)

b^{\frac{5}{9}}

\newline

(C)

b^{\frac{9}{5}}

\newline

(D)

None of the

Understand Properties: To find the equivalent expressions for the fifth root of $b$ to the ninth power, we need to understand the properties of exponents and roots. The fifth root of $b$ to the ninth power can be written as $(b^9)^{1/5}$ .
Evaluate Option A: Now let's evaluate each option given: $\newline$ A) $(b^{5})^{(1/9)}$ can be simplified using the property $(a^m)^n = a^{m*n}$ , which gives us $b^{5*(1/9)} = b^{5/9}$ .
Option B: B) The option ＂B＂ is just the letter ＂B＂ and does not represent any mathematical expression, so it cannot be equivalent to $\sqrt[5]{b^{9}}$ .
Evaluate Option C: C) $b^{(9/5)}$ is already in the form of $b^{m/n}$ , but it is not equivalent to $(b^9)^{1/5}$ because $9/5$ is not equal to $1/5$ .
Consider Option D: D) ＂None of the above＂ is an option to consider only if none of the other options (A, B, C) are correct. Since we have found that option A is equivalent to $\sqrt[5]{b^{9}}$ , option D is not correct.
Identify Equivalent Expression: Therefore, the only expression equivalent to $\sqrt[5]{b^{9}}$ is option A, which is $b^{\frac{5}{9}}$ .