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Which expressions are equivalent to
x^(1.4) ?
Choose all answers that apply:
A
root(5)(x^(7))
B
(root(5)(x))^(7)
C
(x^((1)/(5)))^(7)
D None of the above

Which expressions are equivalent to $x^{1.4}$ ? $\newline$ Choose all answers that apply: $\newline$ A $\sqrt[5]{x^{7}}$ $\newline$ B $(\sqrt[5]{x})^{7}$ $\newline$ C. $\left(x^{\frac{1}{5}}\right)^{7}$ $\newline$ D None of the above

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Identify equivalent linear expressions

Full solution

Q. Which expressions are equivalent to

x^{1.4}

?

\newline

Choose all answers that apply:

\newline

A

\sqrt[5]{x^{7}}

\newline

B

(\sqrt[5]{x})^{7}

\newline

C.

\left(x^{\frac{1}{5}}\right)^{7}

\newline

D None of the above

Understand the given expression: Understand the given expression and the options. $\newline$ We need to find which of the given options are equivalent to $x^{1.4}$ . The exponent $1.4$ can be written as a fraction, which is $\frac{7}{5}$ . So we are looking for expressions that can be simplified to $x^{\frac{7}{5}}$ .
Analyze option A: Analyze option A: $\sqrt[5]{x^{7}}$ . The fifth root of $x$ to the power of $7$ is equivalent to $(x^7)^{\frac{1}{5}}$ . Using the power of a power rule, we multiply the exponents: $7 \times \frac{1}{5} = \frac{7}{5}$ . Therefore, $(x^7)^{\frac{1}{5}}$ is equivalent to $x^{\frac{7}{5}}$ .
Analyze option B: Analyze option B: $(\sqrt[5]{x})^{7}$ . The fifth root of $x$ raised to the power of $7$ is equivalent to $(x^{1/5})^7$ . Using the power of a power rule, we multiply the exponents: $(1/5) \times 7 = 7/5$ . Therefore, $(x^{1/5})^7$ is equivalent to $x^{7/5}$ .
Analyze option C: Analyze option C: $(x^{(\frac{1}{5})})^{7}$ . This option is the same as option B, where $x$ is raised to the power of $\frac{1}{5}$ and then that result is raised to the power of $7$ . As calculated in Step $3$ , this is equivalent to $x^{\frac{7}{5}}$ .
Analyze option D: Analyze option D: None of the above. $\newline$ Since we have already found that options A, B, and C are equivalent to $x^{1.4}$ , option D is incorrect.

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