Which expressions are equivalent to root(7)(v^(3)) ? Choose all answers that apply: A (v^(3))^((1)/(7)) B (root(3)(v))^(7) C. v^((3)/(7)) D None of the above

Question

Which expressions are equivalent to  root(7)(v^(3)) ? Choose all answers that apply: A  (v^(3))^((1)/(7)) B  (root(3)(v))^(7) C.  v^((3)/(7)) D None of the above

Bytelearn · Accepted Answer

Understand given expression: Understand the given expression. The given expression is root(7)(v^(3)), which means the 7th root of v raised to the power of 3.Analyze option A: Analyze option A. Option A is (v^(3))^((1)/(7)). According to the properties of exponents, (a^m)^n = a^(m*n). So, (v^(3))^((1)/(7)) simplifies to v^(3*(1/7)), which is v^(3/7).Compare with given expression: Compare option A with the given expression. Since root(7)(v^(3)) is the same as v^(3/7), option A is equivalent to the given expression.Analyze option B: Analyze option B. Option B is (root(3)(v))^(7). This expression means taking the cube root of v and then raising it to the 7th power, which is not the same as the 7th root of v raised to the power of 3. Therefore, option B is not equivalent to the given expression.Analyze option C: Analyze option C. Option C is v^((3)/(7)). This expression is already in the form of a single exponent and matches the simplified form of the given expression, which is the 7th root of v raised to the power of 3. Therefore, option C is equivalent to the given expression.Analyze option D: Analyze option D. Option D states that none of the above options are equivalent to the given expression. Since we have already found that options A and C are equivalent, option D is incorrect.

Which expressions are equivalent to $\sqrt[7]{v^{3}}$ ? $\newline$ Choose all answers that apply: $\newline$ A $\left(v^{3}\right)^{\frac{1}{7}}$ $\newline$ B $(\sqrt[3]{v})^{7}$ $\newline$ C. $v^{\frac{3}{7}}$ $\newline$ D None of the above

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Which expressions are equivalent to $\sqrt[7]{v^{3}}$ ? $\newline$ Choose all answers that apply: $\newline$ A $\left(v^{3}\right)^{\frac{1}{7}}$ $\newline$ B $(\sqrt[3]{v})^{7}$ $\newline$ C. $v^{\frac{3}{7}}$ $\newline$ D None of the above