Which expressions are equivalent to z^(0.2) ? Choose all answers that apply: A sqrtz B root(5)(z) c (z^(2))^(-10) D None of the above

Understand Expression: Understand the given expression z^(0.2). The given expression z^(0.2) can be rewritten as the 5th root of z because 0.2 is the same as 1/5. So, z^(0.2) = z^(1/5) = root(5)(z).Compare Option A: Compare the given expression to option A. Option A is sqrt(z), which is the same as z^(1/2). This is not equivalent to z^(0.2) because 1/2 is not equal to 1/5.Compare Option B: Compare the given expression to option B. Option B is root(5)(z), which is the same as z^(1/5). This is equivalent to z^(0.2) because 1/5 is equal to 0.2.Compare Option C: Compare the given expression to option C. Option C is (z^(2))^(-10). Using the power of a power rule, we can simplify this expression as z^(2 * -10) = z^(-20). This is not equivalent to z^(0.2) because -20 is not equal to 0.2.Determine Option D: Determine if option D is correct. Option D states ＂None of the above,＂ which is not correct because we have already established that option B is equivalent to z^(0.2).

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Which expressions are equivalent to
z^(0.2) ?
Choose all answers that apply:
A
sqrtz
B
root(5)(z)
c
(z^(2))^(-10)
D None of the above

Which expressions are equivalent to $z^{0.2}$ ? $\newline$ Choose all answers that apply: $\newline$ A $\sqrt{z}$ $\newline$ B $\sqrt[5]{z}$ $\newline$ C $\left(z^{2}\right)^{-10}$ $\newline$ D None of the above

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Math Problems

Algebra 2

Evaluate exponential functions

Full solution

Q. Which expressions are equivalent to

z^{0.2}

\newline

Choose all answers that apply:

\newline

\sqrt{z}

\newline

\sqrt[5]{z}

\newline

\left(z^{2}\right)^{-10}

\newline

D None of the above

Understand Expression: Understand the given expression $z^{0.2}$ . The given expression $z^{0.2}$ can be rewritten as the $5$ th root of $z$ because $0.2$ is the same as $\frac{1}{5}$ . So, $z^{0.2} = z^{\frac{1}{5}} = \sqrt[5]{z}$ .
Compare Option A: Compare the given expression to option A. $\newline$ Option A is $\sqrt{z}$ , which is the same as $z^{\frac{1}{2}}$ . This is not equivalent to $z^{0.2}$ because $\frac{1}{2}$ is not equal to $\frac{1}{5}$ .
Compare Option B: Compare the given expression to option B. $\newline$ Option B is $\sqrt[5]{z}$ , which is the same as $z^{\frac{1}{5}}$ . This is equivalent to $z^{0.2}$ because $\frac{1}{5}$ is equal to $0.2$ .
Compare Option C: Compare the given expression to option C. $\newline$ Option C is $(z^{2})^{-10}$ . Using the power of a power rule, we can simplify this expression as $z^{2 \cdot -10} = z^{-20}$ . This is not equivalent to $z^{0.2}$ because $-20$ is not equal to $0.2$ .
Determine Option D: Determine if option D is correct. $\newline$ Option D states ＂None of the above,＂ which is not correct because we have already established that option B is equivalent to $z^{0.2}$ .