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

Question

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

Bytelearn · Accepted Answer

Understand the 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 to the power of 7 is equivalent to (x^7)^(1/5). Using the power of a power rule, we multiply the exponents: 7 * (1/5) = 7/5. Therefore, (x^7)^(1/5) is equivalent to x^(7/5).Analyze option B: Analyze option B: (root(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) * 7 = 7/5. Therefore, (x^(1/5))^7 is equivalent to x^(7/5).Analyze option C: Analyze option C: (x^((1)/(5)))^(7). This option is the same as option B, where x is raised to the power of 1/5 and then that result is raised to the power of 7. As calculated in Step 3, this is equivalent to x^(7/5).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.

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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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