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

Understand Given Expression: Understand the given expression and the options. 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 7/5. So we are looking for expressions that can be simplified to x^(7/5).Analyze Option A: Analyze option A: root(5)(x^(7)). The fifth root of x^7 can be written as (x^7)^(1/5). Using the property of exponents (a^(m))^n = a^(m*n), we get x^(7*(1/5)) = x^(7/5), which is equivalent to x^(1.4).Analyze Option B: Analyze option B: (root(5)(x))^(7). The fifth root of x can be written as x^(1/5). Raising this to the 7th power using the property of exponents (a^(m))^n = a^(m*n), we get (x^(1/5))^7 = x^((1/5)*7) = x^(7/5), which is also equivalent to x^(1.4).Analyze Option C: Analyze option C: (x^((1)/(5)))^(7). This is similar to option B. The expression (x^(1/5))^7 can be simplified using the property of exponents (a^(m))^n = a^(m*n), which gives us x^((1/5)*7) = x^(7/5), equivalent to x^(1.4).Analyze Option D: Analyze option D: None of the above. 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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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) $(x^{\frac{1}{5}})^7$ $\newline$ (D) None of the above

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Math Problems

Algebra 1

Multiplication with rational exponents

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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)

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

\newline

(D) None of the above

Understand 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 $x^7$ can be written as $(x^7)^{\frac{1}{5}}$ . Using the property of exponents $(a^{m})^n = a^{m*n}$ , we get $x^{7*\left(\frac{1}{5}\right)} = x^{\frac{7}{5}}$ , which is equivalent to $x^{1.4}$ .
Analyze Option B: Analyze option B: $(\sqrt[5]{x})^{7}$ . The fifth root of $x$ can be written as $x^{(1/5)}$ . Raising this to the $7$ th power using the property of exponents $(a^{m})^{n} = a^{m*n}$ , we get $(x^{(1/5)})^{7} = x^{((1/5)*7)} = x^{(7/5)}$ , which is also equivalent to $x^{1.4}$ .
Analyze Option C: Analyze option C: $(x^{(1/5)})^{7}$ . This is similar to option B. The expression $(x^{1/5})^7$ can be simplified using the property of exponents $(a^{m})^{n} = a^{m*n}$ , which gives us $x^{(1/5)*7} = x^{7/5}$ , equivalent to $x^{1.4}$ .
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.