Which expressions are equivalent to k^(-(1)/(6)) ? Choose all answers that apply: A (1)/(k^(6)) B (k^(-1))^((1)/(6)) c root(6)(k^(-1)) D None of the above

Understand given expression: Understand the given expression. The given expression is k^(-(1)/(6)), which means we are looking for expressions that represent the sixth root of 1/k or the reciprocal of the sixth power of k.Analyze option A: Analyze option A. Option A is (1)/(k^(6)). This is not equivalent to k^(-(1)/(6)) because it represents the reciprocal of k raised to the sixth power, not the sixth root of 1/k.Analyze option B: Analyze option B. Option B is (k^(-1))^((1)/(6)). This expression represents the sixth root of k raised to the negative first power, which is equivalent to the sixth root of 1/k. Therefore, option B is equivalent to k^(-(1)/(6)).Analyze option C: Analyze option C. Option C is root(6)(k^(-1)). This expression represents the sixth root of k raised to the negative first power, which is equivalent to the sixth root of 1/k. Therefore, option C is equivalent to k^(-(1)/(6)).Analyze option D: Analyze option D. Option D states ＂None of the above,＂ which is incorrect because we have found that options B and C are equivalent to k^(-(1)/(6)).

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Which expressions are equivalent to
k^(-(1)/(6)) ?
Choose all answers that apply:
A
(1)/(k^(6))
B
(k^(-1))^((1)/(6))
c
root(6)(k^(-1))
D None of the above

Which expressions are equivalent to $k^{-\frac{1}{6}}$ ? $\newline$ Choose all answers that apply: $\newline$ A $\frac{1}{k^{6}}$ $\newline$ B $\left(k^{-1}\right)^{\frac{1}{6}}$ $\newline$ c $\sqrt[6]{k^{-1}}$ $\newline$ D None of the above

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Which expressions are equivalent to

k^{-\frac{1}{6}}

\newline

Choose all answers that apply:

\newline

\frac{1}{k^{6}}

\newline

\left(k^{-1}\right)^{\frac{1}{6}}

\newline

\sqrt[6]{k^{-1}}

\newline

D None of the above

Understand given expression: Understand the given expression. $\newline$ The given expression is $k^{-\frac{1}{6}}$ , which means we are looking for expressions that represent the sixth root of $\frac{1}{k}$ or the reciprocal of the sixth power of $k$ .
Analyze option A: Analyze option A. $\newline$ Option A is $(1)/(k^{6})$ . This is not equivalent to $k^{-(1)/(6)}$ because it represents the reciprocal of $k$ raised to the sixth power, not the sixth root of $1/k$ .
Analyze option B: Analyze option B. $\newline$ Option B is $(k^{-1})^{\frac{1}{6}}$ . This expression represents the sixth root of $k$ raised to the negative first power, which is equivalent to the sixth root of $\frac{1}{k}$ . Therefore, option B is equivalent to $k^{-\frac{1}{6}}$ .
Analyze option C: Analyze option C. $\newline$ Option C is $\sqrt[6]{k^{-1}}$ . This expression represents the sixth root of $k$ raised to the negative first power, which is equivalent to the sixth root of $\frac{1}{k}$ . Therefore, option C is equivalent to $k^{-\left(\frac{1}{6}\right)}$ .
Analyze option D: Analyze option D. $\newline$ Option D states ＂None of the above,＂ which is incorrect because we have found that options B and C are equivalent to $k^{-\frac{1}{6}}$ .